RD Sharma Solutions Class 9 Maths Chapter 2 – Exponents Of Real Numbers (Updated for 2024)

RD Sharma Solutions Class 9 Maths Chapter 2 Exponents Of Real Numbers:  Get your hands on RD Sharma Solutions CBSE Class 9 Maths and start your maths final preparation. Exponents of real numbers are one of the vital sections that need crystal clear concepts. Hence you should start now with RD Sharma Solutions Class 9 Maths Chapter 2 Exponents Of Real Numbers to build a clear picture of what Exponents are.

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RD Sharma Solutions Class 9 Maths Chapter 2 

RD Sharma Solutions Class 9 Maths Chapter 2 – Exponents Of Real Numbers: Exercise wise Solutions

RD Sharma Solutions Class 9 Chapter 2 Exercise 2.1

RD Sharma Solutions Class 9 Chapter 2 Exercise 2.2

Access answers of RD Sharma Solutions Class 9 Maths Chapter 2

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) a^a+ b^b
(ii) a^b + b^a
(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 = 2^a x 3^b x T^c, find a, 6, and c.
Solution:

Question 12.
Given 4725 = 3^a5^b7^c, find:
(i) the integral values of a, b and c
(ii) the value of 2^-a 3^b 7^c
Solution:

Question 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
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 = 2^1/3 + 2^2/3, show that x³ – 6x = 6.
Solution:

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

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

Question 14.
If 3^4x = (81)^-1 and 10^1/y = 0.0001, find the value of 2^-x+4y
Solution:

Question 15.
If 5^3x = 125 and 10^y = 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 2^x x 3^y x 5^z = 2160, find x, y, and z. Hence, compute the value of 3^x x 2^-y x 5^-z.
Solution:

Question 20.
If 1176 = 2^a x 3^b x 7^c, find the values of a, b, and c. Hence, compute the value of 2^a x 3^b 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:
x^m x xⁿ = x^{m +n}

Question 3.
State the quotient law of exponents.
Solution:
x^m ÷ xⁿ = x^{m -n}

Question 4.
State the power law of exponents.
Solution:
(x^m)ⁿ =x^{m x n} = x^mn

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

Question 6.

Solution:

Question 7.
Write the value of 7–√3  x 49−−√3 .
Solution:

Question 8.

Solution:

Question 9.
Write the value of 125×27−−−−−−−√3
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) 15
(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 – y^x-y when x = 2 and y = -2 is
(a) 18
(b) -18
(c) 14
(d) -14
Solution:
x = 2, y = -2
x-y^x-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) the sixth root of the fifth power of x
(c) fifth root of the sixth power of x
(d) the 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) 12
(d) 64²³
Solution:

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

Solution:

Question 7.
When simplified (x^–1 + y^–1)^–1 is equal to

Solution:

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

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

Question 10.
If x^-2= 64, then x¹³ + x°=
(a) 2
(b) 3
(c) 32
(c) 23
Solution:

Question 11.
When simplified ( –127)⁻²³
(a) 9
(b) -9
(c) 19
(d) –19
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)²³  +(150 – 29)¹² ]²
= [(27)²³ + (121)¹² ]²
= [(3³)³ +(11²)¹²]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 10^2y = 25, then 10^-y equals

Solution:

Question 24.
If 9^X + 2 = 240 + 9^X. 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) 2–√
(b) 22–√
(c) 32–√
(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 4^{2x – 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:

Important Topics: RD Sharma Solutions Class 9 Maths Chapter 2 

Let us now have a quick check on the important topics that this chapter covers are-

• Exponents of Real Numbers Introduction
• Integral exponents of a Real Number
• Laws of Integral Exponents
• Rational Exponents of Real Number
• the nth root of a positive Real Number
• Laws of rational exponents

Well, this is it. Here we have compiled everything that you need to finish your CBSE class 9 maths syllabus. If you have any doubts regarding the Class 9 Maths exams, ask in the comments. 

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