# RD Sharma solutions for Mathematics for Class 9 chapter 2 - Exponents of Real Numbers [Latest edition]

## Chapter 2: Exponents of Real Numbers

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4
Exercise 2.1 [Pages 12 - 13]

### RD Sharma solutions for Mathematics for Class 9 Chapter 2 Exponents of Real Numbers Exercise 2.1 [Pages 12 - 13]

Exercise 2.1 | Q 1.1 | Page 12

Simplify the following

3(a^4b^3)^10xx5(a^2b^2)^3

Exercise 2.1 | Q 1.2 | Page 12

Simplify the following

(2x^-2y^3)^3

Exercise 2.1 | Q 1.3 | Page 12

Simplify the following

((4xx10^7)(6xx10^-5))/(8xx10^4)

Exercise 2.1 | Q 1.4 | Page 12

Simplify the following

(4ab^2(-5ab^3))/(10a^2b^2)

Exercise 2.1 | Q 1.5 | Page 12

Simplify the following

((x^2y^2)/(a^2b^3))^n

Exercise 2.1 | Q 1.6 | Page 12

Simplify the following

(a^(3n-9))^6/(a^(2n-4))

Exercise 2.1 | Q 2.1 | Page 12

If a = 3 and b = -2, find the values of :

aa + bb

Exercise 2.1 | Q 2.2 | Page 12

If a = 3 and b = -2, find the values of :

ab + ba

Exercise 2.1 | Q 2.3 | Page 12

If a = 3 and b = -2, find the values of :

(a + b)ab

Exercise 2.1 | Q 3.1 | Page 12

Prove that:

(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1

Exercise 2.1 | Q 3.2 | Page 12

Prove that:

(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1

Exercise 2.1 | Q 4.1 | Page 12

Prove that:

1/(1+x^(a-b))+1/(1+x^(b-a))=1

Exercise 2.1 | Q 4.2 | Page 12

Prove that:

1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))=1

Exercise 2.1 | Q 5.1 | Page 12

Prove that:

(a+b+c)/(a^-1b^-1+b^-1c^-1+c^-1a^-1)=abc

Exercise 2.1 | Q 5.2 | Page 12

Prove that:

(a^-1+b^-1)^-1=(ab)/(a+b)

Exercise 2.1 | Q 6 | Page 12

If abc = 1, show that 1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1

Exercise 2.1 | Q 7.1 | Page 12

Simplify the following:

(3^nxx9^(n+1))/(3^(n-1)xx9^(n-1))

Exercise 2.1 | Q 7.2 | Page 12

Simplify the following:

(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))

Exercise 2.1 | Q 7.3 | Page 12

Simplify the following:

(5^(n+3)-6xx5^(n+1))/(9xx5^x-2^2xx5^n)

Exercise 2.1 | Q 7.4 | Page 12

Simplify the following:

(6(8)^(n+1)+16(2)^(3n-2))/(10(2)^(3n+1)-7(8)^n)

Exercise 2.1 | Q 8.1 | Page 12

Solve the following equation for x:

7^(2x+3)=1

Exercise 2.1 | Q 8.2 | Page 12

Solve the following equation for x:

2^(x+1)=4^(x-3)

Exercise 2.1 | Q 8.3 | Page 12

Solve the following equation for x:

2^(5x+3)=8^(x+3)

Exercise 2.1 | Q 8.4 | Page 12

Solve the following equation for x:

4^(2x)=1/32

Exercise 2.1 | Q 8.5 | Page 12

Solve the following equation for x:

4^(x-1)xx(0.5)^(3-2x)=(1/8)^x

Exercise 2.1 | Q 8.6 | Page 12

Solve the following equation for x:

2^(3x-7)=256

Exercise 2.1 | Q 9.1 | Page 12

Solve the following equations for x:

2^(2x)-2^(x+3)+2^4=0

Exercise 2.1 | Q 9.2 | Page 12

Solve the following equations for x:

3^(2x+4)+1=2.3^(x+2)

Exercise 2.1 | Q 10 | Page 13

If 49392 = a4b2c3, find the values of a, b and c, where a, b and c are different positive primes.

Exercise 2.1 | Q 11 | Page 13

If 1176=2^a3^b7^c, find a, b and c.

Exercise 2.1 | Q 12 | Page 13

Given 4725=3^a5^b7^c, find

(i) the integral values of a, b and c

(ii) the value of 2^-a3^b7^c

Exercise 2.1 | Q 13 | Page 13

If a=xy^(p-1), b=xy^(q-1) and c=xy^(r-1), prove that a^(q-r)b^(r-p)c^(p-q)=1

Exercise 2.2 [Pages 24 - 27]

### RD Sharma solutions for Mathematics for Class 9 Chapter 2 Exponents of Real Numbers Exercise 2.2 [Pages 24 - 27]

Exercise 2.2 | Q 1.1 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

(sqrt(x^-3))^5

Exercise 2.2 | Q 1.2 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

sqrt(x^3y^-2)

Exercise 2.2 | Q 1.3 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

(x^((-2)/3)y^((-1)/2))^2

Exercise 2.2 | Q 1.4 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

(sqrtx)^((-2)/3)sqrt(y^4)divsqrt(xy^((-1)/2))

Exercise 2.2 | Q 1.5 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

root5(243x^10y^5z^10)

Exercise 2.2 | Q 1.6 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

(x^-4/y^-10)^(5/4)

Exercise 2.2 | Q 1.7 | Page 24

Assuming that x, y, z are positive real numbers, simplify the following:

(sqrt2/sqrt3)^5(6/7)^2

Exercise 2.2 | Q 2.1 | Page 24

Simplify:

(16^(-1/5))^(5/2)

Exercise 2.2 | Q 2.2 | Page 24

Simplify:

root5((32)^-3)

Exercise 2.2 | Q 2.3 | Page 24

Simplify:

root3((343)^-2)

Exercise 2.2 | Q 2.4 | Page 24

Simplify:

(0.001)^(1/3)

Exercise 2.2 | Q 2.5 | Page 24

Simplify:

((25)^(3/2)xx(243)^(3/5))/((16)^(5/4)xx(8)^(4/3))

Exercise 2.2 | Q 2.6 | Page 24

Simplify:

(sqrt2/5)^8div(sqrt2/5)^13

Exercise 2.2 | Q 2.7 | Page 24

Simplify:

((5^-1xx7^2)/(5^2xx7^-4))^(7/2)xx((5^-2xx7^3)/(5^3xx7^-5))^(-5/2)

Exercise 2.2 | Q 3.1 | Page 24

Prove that:

sqrt(3xx5^-3)divroot3(3^-1)sqrt5xxroot6(3xx5^6)=3/5

Exercise 2.2 | Q 3.2 | Page 24

Prove that:

9^(3/2)-3xx5^0-(1/81)^(-1/2)=15

Exercise 2.2 | Q 3.3 | Page 24

Prove that:

(1/4)^-2-3xx8^(2/3)xx4^0+(9/16)^(-1/2)=16/3

Exercise 2.2 | Q 3.4 | Page 24

Prove that:

(2^(1/2)xx3^(1/3)xx4^(1/4))/(10^(-1/5)xx5^(3/5))div(3^(4/3)xx5^(-7/5))/(4^(-3/5)xx6)=10

Exercise 2.2 | Q 3.5 | Page 24

Prove that:

sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2

Exercise 2.2 | Q 3.6 | Page 24

Prove that:

(2^n+2^(n-1))/(2^(n+1)-2^n)=3/2

Exercise 2.2 | Q 3.7 | Page 24

Prove that:

(64/125)^(-2/3)+1/(256/625)^(1/4)+(sqrt25/root3 64)=65/16

Exercise 2.2 | Q 3.8 | Page 24

Prove that:

(3^-3xx6^2xxsqrt98)/(5^2xxroot3(1/25)xx(15)^(-4/3)xx3^(1/3))=28sqrt2

Exercise 2.2 | Q 3.9 | Page 24

Prove that:

((0.6)^0-(0.1)^-1)/((3/8)^-1(3/2)^3+((-1)/3)^-1)=(-3)/2

Exercise 2.2 | Q 4.1 | Page 25

Show that:

1/(1+x^(a-b))+1/(1+x^(b-a))=1

Exercise 2.2 | Q 4.2 | Page 25

Show that:

[{x^(a(a-b))/x^(a(a+b))}div{x^(b(b-a))/x^(b(b+a))}]^(a+b)=1

Exercise 2.2 | Q 4.3 | Page 25

Show that:

(x^(1/(a-b)))^(1/(a-c))(x^(1/(b-c)))^(1/(b-a))(x^(1/(c-a)))^(1/(c-b))=1

Exercise 2.2 | Q 4.4 | Page 25

Show that:

(x^(a^2+b^2)/x^(ab))^(a+b)(x^(b^2+c^2)/x^(bc))^(b+c)(x^(c^2+a^2)/x^(ac))^(a+c)=x^(2(a^3+b^3+c^3))

Exercise 2.2 | Q 4.5 | Page 25

Show that:

(x^(a-b))^(a+b)(x^(b-c))^(b+c)(x^(c-a))^(c+a)=1

Exercise 2.2 | Q 4.6 | Page 25

Show that:

{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x

Exercise 2.2 | Q 4.7 | Page 25

Show that:

(a^(x+1)/a^(y+1))^(x+y)(a^(y+2)/a^(z+2))^(y+z)(a^(z+3)/a^(x+3))^(z+x)=1

Exercise 2.2 | Q 4.8 | Page 25

Show that:

(3^a/3^b)^(a+b)(3^b/3^c)^(b+c)(3^c/3^a)^(c+a)=1

Exercise 2.2 | Q 5 | Page 25

If 2x = 3y = 12z, show that 1/z=1/y+2/x

Exercise 2.2 | Q 6 | Page 25

If 2x = 3y = 6-z, show that 1/x+1/y+1/z=0

Exercise 2.2 | Q 7 | Page 25

If ax = by = cz and b2 = ac, show that y=(2zx)/(z+x)

Exercise 2.2 | Q 8 | Page 26

If 3x = 5y = (75)z, show that z=(xy)/(2x+y)

Exercise 2.2 | Q 9 | Page 26

If 27^x=9/3^x, find x.

Exercise 2.2 | Q 10.1 | Page 26

Find the value of x in the following:

2^(5x)div2x=root5(2^20)

Exercise 2.2 | Q 10.2 | Page 26

Find the value of x in the following:

(2^3)^4=(2^2)^x

Exercise 2.2 | Q 10.3 | Page 26

Find the value of x in the following:

(3/5)^x(5/3)^(2x)=125/27

Exercise 2.2 | Q 10.4 | Page 26

Find the value of x in the following:

5^(x-2)xx3^(2x-3)=135

Exercise 2.2 | Q 10.5 | Page 26

Find the value of x in the following:

2^(x-7)xx5^(x-4)=1250

Exercise 2.2 | Q 10.6 | Page 26

Find the value of x in the following:

(root3 4)^(2x+1/2)=1/32

Exercise 2.2 | Q 10.7 | Page 26

Find the value of x in the following:

5^(2x+3)=1

Exercise 2.2 | Q 10.8 | Page 26

Find the value of x in the following:

(13)^(sqrtx)=4^4-3^4-6

Exercise 2.2 | Q 10.9 | Page 26

Find the value of x in the following:

(sqrt(3/5))^(x+1)=125/27

Exercise 2.2 | Q 11 | Page 26

If x=2^(1/3)+2^(2/3), Show that x3 - 6x = 6

Exercise 2.2 | Q 12 | Page 26

Determine (8x)^x,If 9^(x+2)=240+9^x

Exercise 2.2 | Q 13 | Page 26

If 3^(x+1)=9^(x-2), find the value of 2^(1+x)

Exercise 2.2 | Q 14 | Page 26

If 3^(4x) = (81)^-1 and 10^(1/y)=0.0001, find the value of   2^(-x+4y).

Exercise 2.2 | Q 15 | Page 26

If 5^(3x)=125 and 10^y=0.001, find x and y.

Exercise 2.2 | Q 16.1 | Page 26

Solve the following equation:

3^(x+1)=27xx3^4

Exercise 2.2 | Q 16.2 | Page 26

Solve the following equation:

4^(2x)=(root3 16)^(-6/y)=(sqrt8)^2

Exercise 2.2 | Q 16.3 | Page 26

Solve the following equation:

3^(x-1)xx5^(2y-3)=225

Exercise 2.2 | Q 16.4 | Page 26

Solve the following equation:

8^(x+1)=16^(y+2) and, (1/2)^(3+x)=(1/4)^(3y)

Exercise 2.2 | Q 16.5 | Page 26

Solve the following equation:

4^(x-1)xx(0.5)^(3-2x)=(1/8)^x

Exercise 2.2 | Q 16.6 | Page 26

Solve the following equation:

sqrt(a/b)=(b/a)^(1-2x), where a and b are distinct primes.

Exercise 2.2 | Q 17 | Page 26

If a and b are distinct primes such that root3 (a^6b^-4)=a^xb^(2y), find x and y.

Exercise 2.2 | Q 18.1 | Page 26

If a and b are different positive primes such that

((a^-1b^2)/(a^2b^-4))^7div((a^3b^-5)/(a^-2b^3))=a^xb^y, find x and y.

Exercise 2.2 | Q 18.2 | Page 26

If a and b are different positive primes such that

(a+b)^-1(a^-1+b^-1)=a^xb^y, find x + y + 2.

Exercise 2.2 | Q 19 | Page 26

If 2^x xx3^yxx5^z=2160, find x, y and z. Hence, compute the value of 3^x xx2^-yxx5^-z.

Exercise 2.2 | Q 20 | Page 26

If 1176 = 2^axx3^bxx7^c, find the values of a, b and c. Hence, compute the value of 2^axx3^bxx7^-c as a fraction.

Exercise 2.2 | Q 21.1 | Page 27

Simplify:

(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)

Exercise 2.2 | Q 21.2 | Page 27

Simplify:

root(lm)(x^l/x^m)xxroot(mn)(x^m/x^n)xxroot(nl)(x^n/x^l)

Exercise 2.2 | Q 22 | Page 27

Show that:

((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)

Exercise 2.2 | Q 23.1 | Page 27

If a=x^(m+n)y^l, b=x^(n+l)y^m and c=x^(l+m)y^n, Prove that a^(m-n)b^(n-l)c^(l-m)=1

Exercise 2.2 | Q 23.2 | Page 27

If x = a^(m+n), y=a^(n+l) and z=a^(l+m), prove that x^my^nz^l=x^ny^lz^m

Exercise 2.3 [Pages 28 - 29]

### RD Sharma solutions for Mathematics for Class 9 Chapter 2 Exponents of Real Numbers Exercise 2.3 [Pages 28 - 29]

Exercise 2.3 | Q 1 | Page 28

Write $\left( 625 \right)^{- 1/4}$ in decimal form.

Exercise 2.3 | Q 2 | Page 28

State the product law of exponents.

Exercise 2.3 | Q 3 | Page 28

State the quotient law of exponents.

Exercise 2.3 | Q 4 | Page 28

State the power law of exponents.

Exercise 2.3 | Q 5 | Page 28

If 24 × 42 =16x, then find the value of x.

Exercise 2.3 | Q 6 | Page 28

If 3x-1 = 9 and 4y+2 = 64, what is the value  of $\frac{x}{y}$ ?

Exercise 2.3 | Q 7 | Page 28

Write the value of  $\sqrt[3]{7} \times \sqrt[3]{49} .$

Exercise 2.3 | Q 8 | Page 29

Write $\left( \frac{1}{9} \right)^{- 1/2} \times (64 )^{- 1/3}$ as a rational number.

Exercise 2.3 | Q 9 | Page 29

Write the value of $\sqrt[3]{125 \times 27}$.

Exercise 2.3 | Q 10 | Page 29

For any positive real number x, find the value of $\left( \frac{x^a}{x^b} \right)^{a + b} \times \left( \frac{x^b}{x^c} \right)^{b + c} \times \left( \frac{x^c}{x^a} \right)^{c + a}$.

Exercise 2.3 | Q 11 | Page 29

Write the value of $\left\{ 5( 8^{1/3} + {27}^{1/3} )^3 \right\}^{1/4} .$

Exercise 2.3 | Q 12 | Page 29

Simplify $\left[ \left\{ \left( 625 \right)^{- 1/2} \right\}^{- 1/4} \right]^2$

Exercise 2.3 | Q 13 | Page 29

For any positive real number x, write the value of  $\left\{ \left( x^a \right)^b \right\}^\frac{1}{ab} \left\{ \left( x^b \right)^c \right\}^\frac{1}{bc} \left\{ \left( x^c \right)^a \right\}^\frac{1}{ca}$

Exercise 2.3 | Q 14 | Page 29

If (x − 1)3 = 8, What is the value of (x + 1)2 ?

Exercise 2.4 [Pages 29 - 33]

### RD Sharma solutions for Mathematics for Class 9 Chapter 2 Exponents of Real Numbers Exercise 2.4 [Pages 29 - 33]

Exercise 2.4 | Q 1 | Page 29

The value of $\left\{ 2 - 3 (2 - 3 )^3 \right\}^3$ is

• 5

• 125

• 1/5

• -125

Exercise 2.4 | Q 2 | Page 29

The value of x − yx-y when x = 2 and y = −2 is

• 18

• -18

• 14

• -14

Exercise 2.4 | Q 3 | Page 29

The product of the square root of x with the cube root of x is

•  cube root of the square root of x

• sixth root of the fifth power of x

•  fifth root of the sixth power of x

• sixth root of x

Exercise 2.4 | Q 4 | Page 29

The seventh root of x divided by the eighth root of x is

• x

• $\sqrt{x}$

• $\sqrt[56]{x}$

• $\frac{1}{\sqrt[56]{x}}$

Exercise 2.4 | Q 5 | Page 29

The square root of 64 divided by the cube root of 64 is

• 64

• 2

• $\frac{1}{2}$

• 642/3

Exercise 2.4 | Q 6 | Page 30

Which of the following is (are) not equal to $\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{- 1/6}$ ?

• $\left\{ \left( \frac{5}{6} \right)^\frac{1}{5} \right\}^{- \frac{3}{6}}$

• $\frac{1}{\left\{ \left( \frac{5}{6} \right)^{1/5} \right\}^{1/6}}$

• $\left( \frac{6}{5} \right)^{1/30}$

• $\left( \frac{5}{6} \right)^{- 1/30}$

Exercise 2.4 | Q 7 | Page 30

When simplified $( x^{- 1} + y^{- 1} )^{- 1}$ is equal to

• xy

• x+y

• $\frac{xy}{y + x}$

• $\frac{x + y}{xy}$

Exercise 2.4 | Q 8 | Page 30

If $8^{x + 1}$ = 64 , what is the value of $3^{2x + 1}$ ?

• 1

• 3

• 9

• 27

Exercise 2.4 | Q 9 | Page 30

If (23)2 = 4x, then 3x =

• 3

• 6

• 9

• 27

Exercise 2.4 | Q 10 | Page 30

If x-2 = 64, then x1/3+x0 =

• 2

• 3

• 3/2

• 2/3

Exercise 2.4 | Q 11 | Page 30

When simplified $\left( - \frac{1}{27} \right)^{- 2/3}$ is

• 9

• -9

• $\frac{1}{9}$

• $- \frac{1}{9}$

Exercise 2.4 | Q 12 | Page 30

Which one of the following is not equal to $\left( \sqrt[3]{8} \right)^{- 1/2} ?$

• $\sqrt[3]{2}^{- 1/2}$

• $8^{- 1/6}$

• $\frac{1}{(\sqrt[3]{8} )^{1/2}}$

• $\frac{1}{\sqrt{2}}$

Exercise 2.4 | Q 13 | Page 30

Which one of the following is not equal to $\left( \frac{100}{9} \right)^{- 3/2}$?

• $\left( \frac{9}{100} \right)^{3/2}$

• $\left( \frac{1}{\frac{100}{9}} \right)^{3/2}$

• $\frac{3}{10} \times \frac{3}{10} \times \frac{3}{10}$

• $\sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}} \times \sqrt{\frac{100}{9}}$

Exercise 2.4 | Q 14 | Page 30

If a, b, c are positive real numbers, then  $\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a}$ is equal to

• 1

• abc

• $\sqrt{abc}$

• $\frac{1}{abc}$

Exercise 2.4 | Q 15 | Page 30

(2/3)^x (3/2)^(2x)=81/16 then x

• 2

• 3

• 4

• 1

Exercise 2.4 | Q 16 | Page 31

The value of $\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}$ is

• $\frac{1}{2}$

• 2

• $\frac{1}{4}$

• 4

Exercise 2.4 | Q 17 | Page 31

If a, b, c are positive real numbers, then  $\sqrt[5]{3125 a^{10} b^5 c^{10}}$  is equal to

•  5a2bc2

• 25ab2c

•  5a3bc3

• 125a2bc2

Exercise 2.4 | Q 18 | Page 31

If a, m, n are positive ingegers, then $\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}$ is equal to

• amn

• a

• am/n

• 1

Exercise 2.4 | Q 19 | Page 31

If x = 2 and y = 4, then $\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =$

• 4

• 8

• 12

• 2

Exercise 2.4 | Q 20 | Page 31

The value of m for which $\left[ \left\{ \left( \frac{1}{7^2} \right)^{- 2} \right\}^{- 1/3} \right]^{1/4} = 7^m ,$ is

• $- \frac{1}{3}$

• $\frac{1}{4}$

• -3

• 2

Exercise 2.4 | Q 21 | Page 31

The value of $\left\{ \left( 23 + 2^2 \right)^{2/3} + (140 - 19 )^{1/2} \right\}^2 ,$ is

• 196

• 289

• 324

• 400

Exercise 2.4 | Q 22 | Page 31

(256)0.16 × (256)0.09

• 4

• 16

• 64

• 256.25

Exercise 2.4 | Q 23 | Page 31

If 102y = 25, then 10-y equals

• $- \frac{1}{5}$
• $\frac{1}{50}$
• $\frac{1}{625}$
• $\frac{1}{5}$
Exercise 2.4 | Q 24 | Page 31

If 9x+2 = 240 + 9x, then x =

• 0.5

• 0.2

• 0.4

• 0.1

Exercise 2.4 | Q 25 | Page 31

If x is a positive real number and x2 = 2, then x3 =

• $\sqrt{2}$

• 2$\sqrt{2}$

• 3$\sqrt{2}$

• 4

Exercise 2.4 | Q 26 | Page 31

If $\frac{x}{x^{1 . 5}} = 8 x^{- 1}$ and x > 0, then x =

• $\frac{\sqrt{2}}{4}$

• $\sqrt[2]{2}$

• 4

• 64

Exercise 2.4 | Q 27 | Page 32

If $g = t^{2/3} + 4 t^{- 1/2}$ What is the value of g when t = 64?

• $\frac{21}{2}$

• $\frac{33}{2}$

• $16$

• $\frac{257}{16}$

Exercise 2.4 | Q 28 | Page 32

If $4x - 4 x^{- 1} = 24,$ then (2x)x equals

• $5\sqrt{5}$

• $\sqrt{5}$

• $25\sqrt{5}$

• 125

Exercise 2.4 | Q 29 | Page 32

When simplified $(256) {}^{- ( 4^{- 3/2} )}$ is

• 8

• $\frac{1}{8}$

• 2

• $\frac{1}{2}$

Exercise 2.4 | Q 30 | Page 32

If $\frac{3^{2x - 8}}{225} = \frac{5^3}{5^x},$  then x =

• 2

• 3

• 5

• 4

Exercise 2.4 | Q 31 | Page 32

The value of 64-1/3 (641/3-642/3), is

• 1

• $\frac{1}{3}$

• -3

• -2

Exercise 2.4 | Q 32 | Page 32

If $\sqrt{5^n} = 125$ then  5nsqrt64=

• 25

• $\frac{1}{125}$

• 625

• $\frac{1}{5}$

Exercise 2.4 | Q 33 | Page 32

If (16)2x+3 =(64)x+3, then 42x-2 =

• 64

• 256

• 32

• 512

Exercise 2.4 | Q 34 | Page 32

If $2^{- m} \times \frac{1}{2^m} = \frac{1}{4},$ then $\frac{1}{14}\left\{ ( 4^m )^{1/2} + \left( \frac{1}{5^m} \right)^{- 1} \right\}$  is equal to

• $\frac{1}{2}$
• 2

• 4

• $- \frac{1}{4}$

Exercise 2.4 | Q 35 | Page 32

If $\frac{2^{m + n}}{2^{n - m}} = 16$, $\frac{3^p}{3^n} = 81$ and $a = 2^{1/10}$,than  $\frac{a^{2m + n - p}}{( a^{m - 2n + 2p} )^{- 1}} =$

• 2

• $\frac{1}{4}$
• 9

• $\frac{1}{8}$
Exercise 2.4 | Q 36 | Page 32

If $\frac{3^{5x} \times {81}^2 \times 6561}{3^{2x}} = 3^7$  then x =

• 3

• -3

• $\frac{1}{3}$

• $- \frac{1}{3}$

Exercise 2.4 | Q 37 | Page 33

If o <y <x, which statement must be true?

• $\sqrt{x} - \sqrt{y} = \sqrt{x - y}$

• $\sqrt{x} + \sqrt{x} = \sqrt{2x}$

• $x\sqrt{y} = y\sqrt{x}$

• $\sqrt{xy} = \sqrt{x}\sqrt{y}$

Exercise 2.4 | Q 38 | Page 33

If 10x = 64, what is the value of ${10}^\frac{x}{2} + 1 ?$

• 18

• 42

• 80

• 81

Exercise 2.4 | Q 39 | Page 33

$\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^n - 2 \times 5^{n + 1}}$  is equal to

• $\frac{5}{3}$

• $- \frac{5}{3}$

• $\frac{3}{5}$

• $- \frac{3}{5}$

Exercise 2.4 | Q 40 | Page 33

If $\sqrt{2^n} = 1024,$ then ${3^2}^\left( \frac{n}{4} - 4 \right) =$

• 3

• 9

• 27

• 81

## Chapter 2: Exponents of Real Numbers

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4

## RD Sharma solutions for Mathematics for Class 9 chapter 2 - Exponents of Real Numbers

RD Sharma solutions for Mathematics for Class 9 chapter 2 (Exponents of Real Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics for Class 9 chapter 2 Exponents of Real Numbers are Introduction of Real Number, Concept of Irrational Numbers, Real Numbers and Their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.

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