# RD Sharma Class 9th Solutions Chapter 2 Exponents of Real Numbers

In this chapter, we provide RD Sharma Solutions for Class 9th Solutions Chapter 2 Exponents of Real Numbers for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 9th Solutions Chapter 2 Exponents of Real Numbers pdf, free RD Sharma Solutions for Class 9th Solutions Chapter 2 Exponents of Real Numbers book pdf download. Now you will get step by step solution to each question.

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## RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers

### RD Sharma Class 9 Chapter 2 Exponents of Real Numbers Ex 2.1

Question 1.
Simplify the following:

Solution:

Question 2.
If a = 3 and b =-2, find the values of:
(i) aa+ bb
(ii) ab + ba
(iii) (a+b)ab
Solution:

Question 3.
Prove that:

Solution:

Question 4.
Prove that

Solution:

Question 5.
Prove that

Solution:

Question 6.

Solution:

Question 7.
Simplify the following:

Solution:

Question 8.
Solve the following equations for x:

Solution:

Question 9.
Solve the following equations for x:

Solution:

Question 10.
If 49392 = a4b2V3, find the values.of a, b and c, where a, b and c are different positive primes.
Solution:

Question 11.
If 1176 = 2a x 3b x Tc, find a, 6 and c.
Solution:

Question 12.
Given 4725 = 3a5b7c, find:
(i) the integral values of a, b and c
(ii) the value of 2-a 3b 7c
Solution:

Question 13.
If a = xyp-1, b = xy q-1 and c = xyr-1, prove that aq-r br-p cp-q = 1
Solution:

### RD Sharma Class 9 Solutions Chapter 2 Exponents of Real Numbers E x 2.2

Question 1.
Assuming that x, y, z are positive real numbers, simplify each of the following:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Prove that:

Solution:

Question 4.
Show that:

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.
Find the values of x in each  of the following:

Solution:

Question 11.
If x = 21/3 + 22/3, show that x3 – 6x = 6.
Solution:

Question 12.
Determine (8x)x, if 9x+ 2 = 240 + 9x.
Solution:

Question 13.
If 3x+1 = 9x-2, find the value of 21 +x.
Solution:

Question 14.
If 34x = (81)-1 and 101/y = 0.0001, find the value of 2-x+4y
Solution:

Question 15.
If 53x = 125 and 10y = 0.001 find x and y.
Solution:

Question 16.
Solve the following equations:

Solution:

Question 17.

Solution:

Question 18.
If a and b are different positive primes such that

Solution:

Question 19.
If 2x x 3y x 5z = 2160, find x, y and z. Hence, compute the value of 3x x 2-y x 5-z.
Solution:

Question 20.
If 1176 = 2a x 3b x 7c, find the values of a, b and c. Hence, compute the value of 2a x 3b x 7-c as a fraction.
Solution:

Question 21.
Simplify:

Solution:

Question 22.
Show that:

Solution:

Question 23.

Solution:

### RD Sharma Class 9 Chapter 2 Exponents of Real Numbers VSAQS

Question 1.
Write (625)1/4 in decimal form.
Solution:

Question 2.
State the product law of exponents:
Solution:
xm x xn = xm +n

Question 3.
State the quotient law of exponents.
Solution:
xm ÷ xn = xm -n

Question 4.
State the power law of exponents.
Solution:
(xm)n =xm x n = xmn

Question 5.
If 24 x 42 – 16x, then find the value of x.
Solution:

Question 6.

Solution:

Question 7.
Write the value of (sqrt [ 3 ]{ 7 })  x (sqrt [ 3 ]{ 49 }) .
Solution:

Question 8.

Solution:

Question 9.
Write the value of (sqrt [ 3 ]{ 125×27 })
Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.
If (x – 1)3 = 8, what is the value of (x + 1)2?
Solution:

### Class 9 RD Sharma Solutions Chapter 2 Exponents of Real Numbers MCQS

Mark the correct alternative in each of the following:
Question 1.
The value of {2 – 3 (2 – 3)3}3 is
(a) 5
(b) 125
(c) (frac { 1 }{ 5 })
(d) -125
Solution:
{2 – 3 (2 – 3)3}3 = {2 – 3 (-1)3}3
= {2 – 3 x (-1)}3
= (2 + 3)3 = (5)3
= 125    (b)

Question 2.
The value of x – yx-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
Solution:
x = 2, y = -2
x-yx-y = 2 – (-2)2 – (-2)
= 2 – (-2)2 + 2 = 2 – (-2)4
= 2 – (+16) = 2 – 16 = -14        (d)

Question 3.
The product of the square root of x with the cube root of x, is
(a) cube root of the square root of x
(b) sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) sixth root of x
Solution:

Question 4.
The seventh root of x divided by the eighth root of x is

Solution:

Question 5.
The square root of 64 divided by the cube root of 64 is
(a) 64
(b) 2
(c) (frac { 1 }{ 2 })
(d) 64(frac { 2 }{ 3 })
Solution:

Question 6.
Which of the following is (are) not equal to

Solution:

Question 7.
When simplified (x1 + y1)1 is equal to

Solution:

Question 8.
If 8x+1 = 64, what is the value of 3 2x +1?
(a) 1
(b) 3
(c) 9
(d) 27
Solution:

Question 9.
If (23)2 = 4x then   3x =
(a) 3
(b) 6
(c) 9
(d) 27
Solution:

Question 10.
If x-2= 64, then x(frac { 1 }{ 3 }) + x°=
(a) 2
(b) 3
(c) (frac { 3 }{ 2 })
(c) (frac { 2 }{ 3 })
Solution:

Question 11.
When simplified ( –(frac { 1 }{ 27 }))(frac { -2 }{ 3 })
(a) 9
(b) -9
(c) (frac { 1 }{ 9 })
(d) –(frac { 1 }{ 9 })
Solution:

Question 12.
Which one of the following is not equal to

Solution:

Question 13.
Which one of the following is not equal to

Solution:

Question 14.
If a, b, c are positive real numbers, then

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.
The value of {(23 + 22)2/3+ (150 -29)1/2}2  is
(a) 196
(b) 289
(c) 324
(d) 400
Solution:
{(23 + 22)2/3 + (150 – 29)1/2}2
= [(23×4)(frac { 2 }{ 3 })  +(150 – 29)(frac { 1 }{ 2 }) ]2
= [(27)(frac { 2 }{ 3 }) + (121)(frac { 1 }{ 2 }) ]2
= [(33)3 +(112)(frac { 1 }{ 2 })]2 = (9 + 11)2
= (20)2 = 400  (d)

Question 22.
(256)0.16x (256)0.09
(a) 4
(b) 16
(c) 64
(d) 256.25
Solution:

Question 23.
If 102y = 25, then 10-y equals

Solution:

Question 24.
If 9X + 2 = 240 + 9X. then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1
Solution:

Question 25.
If x is a positive real number and x2 = 2, then x3 =
(a) (sqrt { 2 } )
(b) 2(sqrt { 2 } )
(c) 3(sqrt { 2 } )
(d) 4
Solution:

Question 26.

Solution:

Question 27.

Solution:

Question 28.

Solution:

Question 29.

Solution:

Question 30.

Solution:

Question 31.

Solution:

Question 32.

Solution:

Question 33.
If (16)2x + 3 = (64)x + 3 , then 42x – 2  =
(a) 64
(b) 256
(c) 32
(d) 512
Solution:

Question 34.

Solution:

Question 35.

Solution:

Question 36.

Solution:

Question 37.

Solution:

Question 38.

Solution:

Question 39.

Solution:

Question 40.

Solution:

All Chapter RD Sharma Solutions For Class 9 Maths

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