## 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:

RD Sharma Class 9th Solutions Chapter 2 Exponents of Real Numbers Exercise 2.1