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

## Chapter 2 : Exponents of Real Numbers

#### Pages 12 - 13

Q 1.1 | Page 12

Simplify the following

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

Q 1.2 | Page 12

Simplify the following

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

Q 1.3 | Page 12

Simplify the following

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

Q 1.4 | Page 12

Simplify the following

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

Q 1.5 | Page 12

Simplify the following

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

Q 1.6 | Page 12

Simplify the following

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

Q 2.1 | Page 12

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

aa + bb

Q 2.2 | Page 12

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

ab + ba

Q 2.3 | Page 12

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

(a + b)ab

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

Q 3.2 | Page 12

Prove that:

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

Q 4.1 | Page 12

Prove that:

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

Q 5.1 | Page 12

Prove that:

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

Q 5.2 | Page 12

Prove that:

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

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

Q 7.1 | Page 12

Simplify the following:

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

Q 7.2 | Page 12

Simplify the following:

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

Q 7.3 | Page 12

Simplify the following:

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

Q 7.4 | Page 12

Simplify the following:

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

Q 8.1 | Page 12

Solve the following equation for x:

7^(2x+3)=1

Q 8.2 | Page 12

Solve the following equation for x:

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

Q 8.3 | Page 12

Solve the following equation for x:

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

Q 8.4 | Page 12

Solve the following equation for x:

4^(2x)=1/32

Q 8.5 | Page 12

Solve the following equation for x:

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

Q 8.6 | Page 12

Solve the following equation for x:

2^(3x-7)=256

Q 9.1 | Page 13

Solve the following equations for x:

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

Q 9.2 | Page 13

Solve the following equations for x:

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

Q 10 | Page 13

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

Q 11 | Page 13

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

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

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

#### Pages 24 - 27

Q 1.1 | Page 24

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

(sqrt(x^-3))^5

Q 1.2 | Page 24

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

sqrt(x^3y^-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

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))

Q 1.6 | Page 24

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

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

Q 1.7 | Page 24

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

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

Q 2.1 | Page 24

Simplify:

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

Q 2.2 | Page 24

Simplify:

root5((32)^-3)

Q 2.3 | Page 24

Simplify:

root3((343)^-2)

Q 2.4 | Page 24

Simplify:

(0.001)^(1/3)

Q 2.5 | Page 24

Simplify:

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

Q 2.6 | Page 24

Simplify:

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

Q 2.7 | Page 24

Simplify:

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

Q 3.1 | Page 24

Prove that:

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

Q 3.2 | Page 24

Prove that:

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

Q 3.3 | Page 24

Prove that:

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

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

Q 3.5 | Page 24

Prove that:

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

Q 3.6 | Page 24

Prove that:

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

Q 3.7 | Page 24

Prove that:

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

Q 3.8 | Page 24

Prove that:

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

Q 3.9 | Page 24

Prove that:

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

Q 4.1 | Page 25

Show that:

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

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

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

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))

Q 4.5 | Page 25

Show that:

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

Q 4.6 | Page 25

Show that:

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

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

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

Q 5 | Page 25

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

Q 6 | Page 25

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

Q 7 | Page 25

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

Q 8 | Page 26

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

Q 9 | Page 26

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

Q 10.1 | Page 26

Find the value of x in the following:

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

Q 10.2 | Page 26

Find the value of x in the following:

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

Q 10.3 | Page 26

Find the value of x in the following:

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

Q 10.4 | Page 26

Find the value of x in the following:

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

Q 10.5 | Page 26

Find the value of x in the following:

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

Q 10.6 | Page 26

Find the value of x in the following:

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

Q 10.7 | Page 26

Find the value of x in the following:

5^(2x+3)=1

Q 10.8 | Page 26

Find the value of x in the following:

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

Q 10.9 | Page 26

Find the value of x in the following:

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

Q 11 | Page 26

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

Q 12 | Page 26

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

Q 13 | Page 26

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

Q 14 | Page 26

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

Q 15 | Page 26

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

Q 16.1 | Page 26

Solve the following equation:

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

Q 16.2 | Page 26

Solve the following equation:

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

Q 16.3 | Page 26

Solve the following equation:

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

Q 16.4 | Page 26

Solve the following equation:

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

Q 16.5 | Page 26

Solve the following equation:

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

Q 16.6 | Page 26

Solve the following equation:

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

Q 17 | Page 26

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

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.

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.

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.

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.

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)

Q 21.2 | Page 27

Simplify:

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

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)

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

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

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

RD Sharma solutions for Class 9 Maths 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 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 9 Mathematics chapter 2 Exponents of Real Numbers are Introduction of Real Number, 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.

Using RD Sharma Class 9 solutions Exponents of Real Numbers exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

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