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

## Mathematics for Class 9 by R D Sharma (2018-19 Session)

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session) ## Chapter 2: Exponents of Real Numbers

Ex. 2.10Ex. 2.20Others

#### Chapter 2: Exponents of Real Numbers Exercise 2.10 solutions [Pages 12 - 13]

Ex. 2.10 | Q 1.1 | Page 12

Simplify the following

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

Ex. 2.10 | Q 1.2 | Page 12

Simplify the following

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

Ex. 2.10 | Q 1.3 | Page 12

Simplify the following

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

Ex. 2.10 | Q 1.4 | Page 12

Simplify the following

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

Ex. 2.10 | Q 1.5 | Page 12

Simplify the following

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

Ex. 2.10 | Q 1.6 | Page 12

Simplify the following

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

Ex. 2.10 | Q 2.1 | Page 12

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

aa + bb

Ex. 2.10 | Q 2.2 | Page 12

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

ab + ba

Ex. 2.10 | Q 2.3 | Page 12

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

(a + b)ab

Ex. 2.10 | 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

Ex. 2.10 | Q 3.2 | Page 12

Prove that:

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

Ex. 2.10 | Q 4.1 | Page 12

Prove that:

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

Ex. 2.10 | 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

Ex. 2.10 | Q 5.1 | Page 12

Prove that:

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

Ex. 2.10 | Q 5.2 | Page 12

Prove that:

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

Ex. 2.10 | 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

Ex. 2.10 | Q 7.1 | Page 12

Simplify the following:

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

Ex. 2.10 | Q 7.2 | Page 12

Simplify the following:

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

Ex. 2.10 | Q 7.3 | Page 12

Simplify the following:

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

Ex. 2.10 | Q 7.4 | Page 12

Simplify the following:

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

Ex. 2.10 | Q 8.1 | Page 12

Solve the following equation for x:

7^(2x+3)=1

Ex. 2.10 | Q 8.2 | Page 12

Solve the following equation for x:

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

Ex. 2.10 | Q 8.3 | Page 12

Solve the following equation for x:

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

Ex. 2.10 | Q 8.4 | Page 12

Solve the following equation for x:

4^(2x)=1/32

Ex. 2.10 | Q 8.5 | Page 12

Solve the following equation for x:

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

Ex. 2.10 | Q 8.6 | Page 12

Solve the following equation for x:

2^(3x-7)=256

Ex. 2.10 | Q 9.1 | Page 12

Solve the following equations for x:

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

Ex. 2.10 | Q 9.2 | Page 12

Solve the following equations for x:

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

Ex. 2.10 | Q 10 | Page 13

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

Ex. 2.10 | Q 11 | Page 13

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

Ex. 2.10 | 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

Ex. 2.10 | 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

#### Chapter 2: Exponents of Real Numbers Exercise 2.20 solutions [Pages 24 - 27]

Ex. 2.20 | Q 1.1 | Page 24

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

(sqrt(x^-3))^5

Ex. 2.20 | Q 1.2 | Page 24

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

sqrt(x^3y^-2)

Ex. 2.20 | Q 1.3 | Page 24

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

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

Ex. 2.20 | 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))

Ex. 2.20 | Q 1.5 | Page 24

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

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

Ex. 2.20 | Q 1.6 | Page 24

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

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

Ex. 2.20 | Q 1.7 | Page 24

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

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

Ex. 2.20 | Q 2.1 | Page 24

Simplify:

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

Ex. 2.20 | Q 2.2 | Page 24

Simplify:

root5((32)^-3)

Ex. 2.20 | Q 2.3 | Page 24

Simplify:

root3((343)^-2)

Ex. 2.20 | Q 2.4 | Page 24

Simplify:

(0.001)^(1/3)

Ex. 2.20 | Q 2.5 | Page 24

Simplify:

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

Ex. 2.20 | Q 2.6 | Page 24

Simplify:

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

Ex. 2.20 | Q 2.7 | Page 24

Simplify:

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

Ex. 2.20 | Q 3.1 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.2 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.3 | Page 24

Prove that:

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

Ex. 2.20 | 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

Ex. 2.20 | Q 3.5 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.6 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.7 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.8 | Page 24

Prove that:

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

Ex. 2.20 | Q 3.9 | Page 24

Prove that:

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

Ex. 2.20 | Q 4.1 | Page 25

Show that:

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

Ex. 2.20 | 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

Ex. 2.20 | 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

Ex. 2.20 | 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))

Ex. 2.20 | Q 4.5 | Page 25

Show that:

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

Ex. 2.20 | Q 4.6 | Page 25

Show that:

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

Ex. 2.20 | 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

Ex. 2.20 | 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

Ex. 2.20 | Q 5 | Page 25

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

Ex. 2.20 | Q 6 | Page 25

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

Ex. 2.20 | Q 7 | Page 25

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

Ex. 2.20 | Q 8 | Page 26

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

Ex. 2.20 | Q 9 | Page 26

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

Ex. 2.20 | Q 10.1 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.2 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.3 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.4 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.5 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.6 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.7 | Page 26

Find the value of x in the following:

5^(2x+3)=1

Ex. 2.20 | Q 10.8 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 10.9 | Page 26

Find the value of x in the following:

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

Ex. 2.20 | Q 11 | Page 26

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

Ex. 2.20 | Q 12 | Page 26

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

Ex. 2.20 | Q 13 | Page 26

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

Ex. 2.20 | Q 14 | Page 26

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

Ex. 2.20 | Q 15 | Page 26

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

Ex. 2.20 | Q 16.1 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 16.2 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 16.3 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 16.4 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 16.5 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 16.6 | Page 26

Solve the following equation:

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

Ex. 2.20 | Q 17 | Page 26

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

Ex. 2.20 | 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.

Ex. 2.20 | 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.

Ex. 2.20 | 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.

Ex. 2.20 | 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.

Ex. 2.20 | 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)

Ex. 2.20 | Q 21.2 | Page 27

Simplify:

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

Ex. 2.20 | 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)

Ex. 2.20 | 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

Ex. 2.20 | 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

#### Chapter 2: Exponents of Real Numbers solutions [Pages 28 - 29]

Q 1 | Page 28

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

Q 2 | Page 28

State the product law of exponents.

Q 3 | Page 28

State the quotient law of exponents.

Q 4 | Page 28

State the power law of exponents.

Q 5 | Page 28

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

Q 6 | Page 28

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

Q 7 | Page 28

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

Q 8 | Page 29

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

Q 9 | Page 29

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

Q 10 | Page 29

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

Q 11 | Page 29

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

Q 12 | Page 29

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

Q 13 | Page 29

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

Q 14 | Page 29

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

#### Chapter 2: Exponents of Real Numbers solutions [Pages 29 - 33]

Q 1 | Page 29

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

• 5

• 125

• 1/5

• -125

Q 2 | Page 29

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

• 18

• -18

• 14

• -14

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

Q 4 | Page 29

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

• x

• $\sqrt{x}$

• $\sqrt{x}$

• $\frac{1}{\sqrt{x}}$

Q 5 | Page 29

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

• 64

• 2

• $\frac{1}{2}$

• 642/3

Q 6 | Page 30

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

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

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

• $\left( \frac{6}{5} \right)^{1/30}$

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

Q 7 | Page 30

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

• xy

• x+y

• $\frac{xy}{y + x}$

• $\frac{x + y}{xy}$

Q 8 | Page 30

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

• 1

• 3

• 9

• 27

Q 9 | Page 30

If (23)2 = 4x, then 3x =

• 3

• 6

• 9

• 27

Q 10 | Page 30

If x-2 = 64, then x1/3+x0 =

• 2

• 3

• 3/2

• 2/3

Q 11 | Page 30

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

• 9

• -9

• $\frac{1}{9}$

• $- \frac{1}{9}$

Q 12 | Page 30

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

• $\sqrt{2}^{- 1/2}$

• $8^{- 1/6}$

• $\frac{1}{(\sqrt{8} )^{1/2}}$

• $\frac{1}{\sqrt{2}}$

Q 13 | Page 30

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

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

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

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

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

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

• $\sqrt{abc}$

• $\frac{1}{abc}$

Q 15 | Page 30

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

• 2

• 3

• 4

• 1

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

Q 17 | Page 31

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

•  5a2bc2

• 25ab2c

•  5a3bc3

• 125a2bc2

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

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

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

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

Q 22 | Page 31

(256)0.16 × (256)0.09

• 4

• 16

• 64

• 256.25

Q 23 | Page 31

If 102y = 25, then 10-y equals

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

If 9x+2 = 240 + 9x, then x =

• 0.5

• 0.2

• 0.4

• 0.1

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

Q 26 | Page 31

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

• $\frac{\sqrt{2}}{4}$

• $\sqrt{2}$

• 4

• 64

Q 27 | Page 32

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

• $\frac{21}{2}$

• $\frac{33}{2}$

• $16$

• $\frac{257}{16}$

Q 28 | Page 32

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

• $5\sqrt{5}$

• $\sqrt{5}$

• $25\sqrt{5}$

• 125

Q 29 | Page 32

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

• 8

• $\frac{1}{8}$

• 2

• $\frac{1}{2}$

Q 30 | Page 32

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

• 2

• 3

• 5

• 4

Q 31 | Page 32

The value of 64-1/3 (641/3-642/3), is

• 1

• $\frac{1}{3}$

• -3

• -2

Q 32 | Page 32

If $\sqrt{5^n} = 125$ then  5nsqrt64=

• 25

• $\frac{1}{125}$

• 625

• $\frac{1}{5}$

Q 33 | Page 32

If (16)2x+3 =(64)x+3, then 42x-2 =

• 64

• 256

• 32

• 512

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

• $- \frac{1}{4}$

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

• $\frac{1}{8}$
Q 36 | Page 32

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

• 3

• -3

• $\frac{1}{3}$

• $- \frac{1}{3}$

Q 37 | Page 33

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

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

• $\sqrt{x} + \sqrt{x} = \sqrt{2x}$

• $x\sqrt{y} = y\sqrt{x}$

• $\sqrt{xy} = \sqrt{x}\sqrt{y}$

Q 38 | Page 33

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

• 18

• 42

• 80

• 81

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

• $\frac{5}{3}$

• $- \frac{5}{3}$

• $\frac{3}{5}$

• $- \frac{3}{5}$

Q 40 | Page 33

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

• 3

• 9

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## Chapter 2: Exponents of Real Numbers

Ex. 2.10Ex. 2.20Others

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