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# RD Sharma solutions for Class 8 Maths chapter 2 - Powers [Latest edition]

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#### Chapters ## Chapter 2: Powers

Ex. 2.1Ex. 2.2Ex. 2.3Others

### RD Sharma solutions for Class 8 Maths Chapter 2 Powers 2.1 [Page 8]

Ex. 2.1 | Q 1.1 | Page 8

Express the following as a rational number of the form $\frac{p}{q},$ where p and q are integers and q ≠ 0.

2−3

Ex. 2.1 | Q 1.2 | Page 8

Express the following as a rational number of the form $\frac{p}{q},$ where p and q are integers and q ≠ 0. (−4)−2

Ex. 2.1 | Q 1.3 | Page 8

Express the following as a rational number of the form $\frac{p}{q},$ where p and q are integers and q ≠ 0.

$\frac{1}{3^{- 2}}$

Ex. 2.1 | Q 1.4 | Page 8

Express the following as a rational number of the form $\frac{p}{q},$ where p and q are integers and q ≠ 0.

$\left( \frac{1}{2} \right)^{- 5}$

Ex. 2.1 | Q 1.5 | Page 8

Express the following as a rational number of the form $\frac{p}{q},$ where p and q are integers and q ≠ 0.

$\left( \frac{2}{3} \right)^{- 2}$
Ex. 2.1 | Q 2.1 | Page 8

Find the value of the following:
3−1 + 4−1

Ex. 2.1 | Q 2.2 | Page 8

Find the value of the following:
(30 + 4−1) × 22

Ex. 2.1 | Q 2.3 | Page 8

Find the value of the following:
(3−1 + 4−1 + 5−1)0

Ex. 2.1 | Q 2.4 | Page 8

Find the value of the following:
$\left\{ \left( \frac{1}{3} \right)^{- 1} - \left( \frac{1}{4} \right)^{- 1} \right\}^{- 1}$

Ex. 2.1 | Q 3.1 | Page 8

Find the value of the following:

$\left( \frac{1}{2} \right)^{- 1} + \left( \frac{1}{3} \right)^{- 1} + \left( \frac{1}{4} \right)^{- 1}$

Ex. 2.1 | Q 3.2 | Page 8

Find the value of the following:

$\left( \frac{1}{2} \right)^{- 2} + \left( \frac{1}{3} \right)^{- 2} + \left( \frac{1}{4} \right)^{- 2}$
Ex. 2.1 | Q 3.3 | Page 8

Find the value of the following:

(2−1 × 4−1) ÷ 2−2
Ex. 2.1 | Q 3.4 | Page 8

Find the value of the following:

(5−1 × 2−1) ÷ 6−1
Ex. 2.1 | Q 4.1 | Page 8

Simplify:

$\left( 4^{- 1} \times 3^{- 1} \right)^2$
Ex. 2.1 | Q 4.2 | Page 8

Simplify:

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

Ex. 2.1 | Q 4.3 | Page 8

Simplify:

$\left( 2^{- 1} + 3^{- 1} \right)^{- 1}$
Ex. 2.1 | Q 4.4 | Page 8

Simplify:
$\left( 3^{- 1} \times 4^{- 1} \right)^{- 1} \times 5^{- 1}$

Ex. 2.1 | Q 5.1 | Page 8

Simplify:

$\left( 3^2 + 2^2 \right) \times \left( \frac{1}{2} \right)^3$
Ex. 2.1 | Q 5.2 | Page 8

Simplify:

$\left( 3^2 - 2^2 \right) \times \left( \frac{2}{3} \right)^{- 3}$
Ex. 2.1 | Q 5.3 | Page 8

Simplify:

$\left[ \left( \frac{1}{3} \right)^{- 3} - \left( \frac{1}{2} \right)^{- 3} \right] \div \left( \frac{1}{4} \right)^{- 3}$
Ex. 2.1 | Q 5.4 | Page 8

Simplify:

$\left( 2^2 + 3^2 - 4^2 \right) \div \left( \frac{3}{2} \right)^2$
Ex. 2.1 | Q 6 | Page 8

By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?

Ex. 2.1 | Q 7 | Page 8

By what number should $\left( \frac{1}{2} \right)^{- 1}$ be multiplied so that the product may be equal to $\left( - \frac{4}{7} \right)^{- 1} ?$

Ex. 2.1 | Q 8 | Page 8

By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?

### RD Sharma solutions for Class 8 Maths Chapter 2 Powers 2.2 [Pages 18 - 19]

Ex. 2.2 | Q 1.1 | Page 18

Write the following in exponential form:

$\left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1} \times \left( \frac{3}{2} \right)^{- 1}$
Ex. 2.2 | Q 1.2 | Page 18

Write the following in exponential form:

$\left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2} \times \left( \frac{2}{5} \right)^{- 2}$

Ex. 2.2 | Q 2.1 | Page 18

Evaluate:
5−2

Ex. 2.2 | Q 2.2 | Page 18

Evaluate:
(−3)−2

Ex. 2.2 | Q 2.3 | Page 18

Evaluate:
$\left( \frac{1}{3} \right)^{- 4}$

Ex. 2.2 | Q 2.4 | Page 18

Evaluate:
$\left( \frac{- 1}{2} \right)^{- 1}$

Ex. 2.2 | Q 3.1 | Page 18

Express the following as a rational number in the form $\frac{p}{q}:$

6−1

Ex. 2.2 | Q 3.2 | Page 18

Express the following as a rational number in the form $\frac{p}{q}:$

(−7)−1

Ex. 2.2 | Q 3.3 | Page 18

Express the following as a rational number in the form $\frac{p}{q}:$

$\left( \frac{1}{4} \right)^{- 1}$
Ex. 2.2 | Q 3.4 | Page 18

Express the following as a rational number in the form $\frac{p}{q}:$

$( - 4 )^{- 1} \times \left( \frac{- 3}{2} \right)^{- 1}$
Ex. 2.2 | Q 3.5 | Page 18

Express the following as a rational number in the form $\frac{p}{q}:$

$\left( \frac{3}{5} \right)^{- 1} \times \left( \frac{5}{2} \right)^{- 1}$
Ex. 2.2 | Q 4.1 | Page 18

Simplify:
$\left\{ 4^{- 1} \times 3^{- 1} \right\}^2$

Ex. 2.2 | Q 4.2 | Page 18

Simplify:
$\left\{ 5^{- 1} \div 6^{- 1} \right\}^3$

Ex. 2.2 | Q 4.3 | Page 18

Simplify:

$\left( 2^{- 1} + 3^{- 1} \right)^{- 1}$
Ex. 2.2 | Q 4.4 | Page 18

Simplify:

$\left\{ 3^{- 1} \times 4^{- 1} \right\}^{- 1} \times 5^{- 1}$

Ex. 2.2 | Q 4.5 | Page 18

Simplify:

$\left( 4^{- 1} - 5^{- 1} \right) \div 3^{- 1}$

Ex. 2.2 | Q 5.1 | Page 18

Express the following rational numbers with a negative exponent:

$\left( \frac{1}{4} \right)^3$
Ex. 2.2 | Q 5.2 | Page 18

Express the following rational numbers with a negative exponent:

$3^5$
Ex. 2.2 | Q 5.3 | Page 18

Express the following rational numbers with a negative exponent:

$\left( \frac{3}{5} \right)^4$
Ex. 2.2 | Q 5.4 | Page 18

Express the following rational numbers with a negative exponent:

$\left\{ \left( \frac{3}{2} \right)^4 \right\}^{- 3}$
Ex. 2.2 | Q 5.5 | Page 18

Express the following rational numbers with a negative exponent:

$\left\{ \left( \frac{7}{3} \right)^4 \right\}^{- 3}$
Ex. 2.2 | Q 6.1 | Page 19

Express the following rational numbers with a positive exponent:

$\left( \frac{3}{4} \right)^{- 2}$
Ex. 2.2 | Q 6.2 | Page 19

Express the following rational numbers with a positive exponent:

$\left( \frac{5}{4} \right)^{- 3}$
Ex. 2.2 | Q 6.3 | Page 19

Express the following rational numbers with a positive exponent:

$4^3 \times 4^{- 9}$
Ex. 2.2 | Q 6.4 | Page 19

Express the following rational numbers with a positive exponent:

$\left\{ \left( \frac{4}{3} \right)^{- 3} \right\}^{- 4}$
Ex. 2.2 | Q 6.5 | Page 19

Express the following rational numbers with a positive exponent:

$\left\{ \left( \frac{3}{2} \right)^4 \right\}^{- 2}$
Ex. 2.2 | Q 7.1 | Page 19

Simplify:

$\left\{ \left( \frac{1}{3} \right)^{- 3} - \left( \frac{1}{2} \right)^{- 3} \right\} \div \left( \frac{1}{4} \right)^{- 3}$
Ex. 2.2 | Q 7.2 | Page 19

Simplify:

$\left( 3^2 - 2^2 \right) \times \left( \frac{2}{3} \right)^{- 3}$
Ex. 2.2 | Q 7.3 | Page 19

Simplify:

$\left\{ \left( \frac{1}{2} \right)^{- 1} \times ( - 4 )^{- 1} \right\}^{- 1}$
Ex. 2.2 | Q 7.4 | Page 19

Simplify:

$\left[ \left\{ \left( \frac{- 1}{4} \right)^2 \right\}^{- 2} \right]^{- 1}$
Ex. 2.2 | Q 7.5 | Page 19

Simplify:

$\left\{ \left( \frac{2}{3} \right)^2 \right\}^3 \times \left( \frac{1}{3} \right)^{- 4} \times 3^{- 1} \times 6^{- 1}$
Ex. 2.2 | Q 8 | Page 19

By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?

Ex. 2.2 | Q 9 | Page 19

By what number should $\left( \frac{1}{2} \right)^{- 1}$ be multiplied so that the product may be equal to $\left( \frac{- 4}{7} \right)^{- 1} ?$

Ex. 2.2 | Q 10 | Page 19

By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?

Ex. 2.2 | Q 11 | Page 19

By what number should $\left( \frac{5}{3} \right)^{- 2}$ be multiplied so that the product may be $\left( \frac{7}{3} \right)^{- 1} ?$

Ex. 2.2 | Q 12.1 | Page 19

Find x, if $\left( \frac{1}{4} \right)^{- 4} \times \left( \frac{1}{4} \right)^{- 8} = \left( \frac{1}{4} \right)^{- 4x}$

Ex. 2.2 | Q 12.2 | Page 19

Find x, if
$\left( \frac{- 1}{2} \right)^{- 19} \times \left( \frac{- 1}{2} \right)^8 = \left( \frac{- 1}{2} \right)^{- 2x + 1}$

Ex. 2.2 | Q 12.3 | Page 19

Find x, if

$\left( \frac{3}{2} \right)^{- 3} \times \left( \frac{3}{2} \right)^5 = \left( \frac{3}{2} \right)^{2x + 1}$
Ex. 2.2 | Q 12.4 | Page 19

Find x, if

$\left( \frac{2}{5} \right)^{- 3} \times \left( \frac{2}{5} \right)^{15} = \left( \frac{2}{5} \right)^{2 + 3x}$
Ex. 2.2 | Q 12.5 | Page 19

Find x, if

$\left( \frac{5}{4} \right)^{- x} \div \left( \frac{5}{4} \right)^{- 4} = \left( \frac{5}{4} \right)^5$
Ex. 2.2 | Q 12.6 | Page 19

Find x, if

$\left( \frac{8}{3} \right)^{2x + 1} \times \left( \frac{8}{3} \right)^5 = \left( \frac{8}{3} \right)^{x + 2}$
Ex. 2.2 | Q 13.1 | Page 19

if $x = \left( \frac{3}{2} \right)^2 \times \left( \frac{2}{3} \right)^{- 4}$, find the value of x−2.

Ex. 2.2 | Q 13.2 | Page 19

If $x = \left( \frac{4}{5} \right)^{- 2} \div \left( \frac{1}{4} \right)^2$, find the value of x−1.

Ex. 2.2 | Q 14 | Page 19

Find the value of x for which 52x ÷ 5−3 = 55.

### RD Sharma solutions for Class 8 Maths Chapter 2 Powers 2.3 [Page 22]

Ex. 2.3 | Q 1.1 | Page 22

Express the following numbers in standard form:
6020000000000000

Ex. 2.3 | Q 1.2 | Page 22

Express the following numbers in standard form:
0.00000000000943

Ex. 2.3 | Q 1.3 | Page 22

Express the following numbers in standard form:
0.00000000085

Ex. 2.3 | Q 1.4 | Page 22

Express the following numbers in standard form:
846 × 107

Ex. 2.3 | Q 1.5 | Page 22

Express the following numbers in standard form:
3759 × 10−4

Ex. 2.3 | Q 1.6 | Page 22

Express the following numbers in standard form:
0.00072984

Ex. 2.3 | Q 1.7 | Page 22

Express the following numbers in standard form:
0.000437 × 104

Ex. 2.3 | Q 1.8 | Page 22

Express the following numbers in standard form:
4 ÷ 100000

Ex. 2.3 | Q 2.1 | Page 22

Write the following numbers in the usual form:
4.83 × 107

Ex. 2.3 | Q 2.2 | Page 22

Write the following numbers in the usual form:
3.02 × 10−6

Ex. 2.3 | Q 2.3 | Page 22

Write the following numbers in the usual form:
4.5 × 104

Ex. 2.3 | Q 2.4 | Page 22

Write the following numbers in the usual form:
3 × 10−8

Ex. 2.3 | Q 2.5 | Page 22

Write the following numbers in the usual form:
1.0001 × 109

Ex. 2.3 | Q 2.6 | Page 22

Write the following numbers in the usual form:
5.8 × 102

Ex. 2.3 | Q 2.7 | Page 22

Write the following numbers in the usual form:
3.61492 × 106

Ex. 2.3 | Q 2.8 | Page 22

Write the following numbers in the usual form:
3.25 × 10−7

### RD Sharma solutions for Class 8 Maths Chapter 2 Powers [Pages 22 - 24]

Q 1 | Page 22

Square of $\left( \frac{- 2}{3} \right)$ is

• $- \frac{2}{3}$

• $\frac{2}{3}$

• $- \frac{4}{9}$

• $\frac{4}{9}$

Q 2 | Page 22

Cube of $\frac{- 1}{2}$ is

• $\frac{1}{8}$

• $\frac{1}{16}$

• $- \frac{1}{8}$

• $\frac{- 1}{16}$

Q 3 | Page 23

Which of the following is not equal to $\left( \frac{- 3}{5} \right)^4 ?$

• $\frac{( - 3 )^4}{5^4}$

• $\frac{3^4}{( - 5 )^4}$

• $- \frac{3^4}{5^4}$

• $\frac{- 3}{5} \times \frac{- 3}{5} \times \frac{- 3}{5} \times \frac{- 3}{5}$

Q 4 | Page 23

Which  of the following is not reciprocal of $\left( \frac{2}{3} \right)^4 ?$

• $\left( \frac{3}{2} \right)^4$

• $\left( \frac{2}{3} \right)^{- 4}$

• $\left( \frac{3}{2} \right)^{- 4}$

• $\frac{3^4}{2^4}$

Q 5 | Page 23

Which of the following numbers is not equal to $\frac{- 8}{27}?$
(a) $\left( \frac{2}{3} \right)^{- 3}$

(b) $- \left( \frac{2}{3} \right)^3$

(c) $\left( - \frac{2}{3} \right)^3$

(d) $\left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right) \times \left( \frac{- 2}{3} \right)$

Q 6 | Page 23
$\left( \frac{2}{3} \right)^{- 5}$ is equal to
• $\left( \frac{- 2}{3} \right)^5$

• $\left( \frac{3}{2} \right)^5$
• $\frac{2x - 5}{3}$
• $\frac{2x - 5}{3}$
Q 7 | Page 23
$\left( \frac{- 1}{2} \right)^5 \times \left( \frac{- 1}{2} \right)^3$ is equal to
• $\left( \frac{- 1}{2} \right)^8$

• $- \left( \frac{1}{2} \right)^8$

• $\left( \frac{1}{4} \right)^8$

• $\left( - \frac{1}{2} \right)^{15}$

Q 8 | Page 23
$\left( \frac{- 1}{5} \right)^3 \div \left( \frac{- 1}{5} \right)^8$  is equal to
• $\left( - \frac{1}{5} \right)^5$

• $\left( - \frac{1}{5} \right)^{11}$

• $( - 5 )^5$

• $\left( \frac{1}{5} \right)^5$

Q 9 | Page 23
$\left( \frac{- 2}{5} \right)^7 \div \left( \frac{- 2}{5} \right)^5$ is equal to
• $\frac{4}{25}$

• $\frac{- 4}{25}$

• $\left( \frac{- 2}{5} \right)^{12}$

• $\frac{25}{4}$

Q 10 | Page 23
$\left\{ \left( \frac{1}{3} \right)^2 \right\}^4$ is equal to
• $\left( \frac{1}{3} \right)^6$

• $\left( \frac{1}{3} \right)^8$

• $\left( \frac{1}{3} \right)^{24}$

• $\left( \frac{1}{3} \right)^{16}$

Q 11 | Page 24
$\left( \frac{1}{5} \right)^0$  is equal to
• 0

• $\frac{1}{5}$

• 1

• 5

Q 12 | Page 24
$\left( \frac{- 3}{2} \right)^{- 1}$ is equal to

• $\frac{2}{3}$

• $- \frac{2}{3}$

• $\frac{3}{2}$

• none of these

Q 13 | Page 24
$\left( \frac{2}{3} \right)^{- 5} \times \left( \frac{5}{7} \right)^{- 5}$ is equal to
• $\left( \frac{2}{3} \times \frac{5}{7} \right)^{- 10}$

• $\left( \frac{2}{3} \times \frac{5}{7} \right)^{- 5}$

• $\left( \frac{2}{3} \times \frac{5}{7} \right)^{25}$

• $\left( \frac{2}{3} \times \frac{5}{7} \right)^{- 25}$

Q 14 | Page 24

$\left( \frac{3}{4} \right)^5 \div \left( \frac{5}{3} \right)^5$ is equal to

• $\left( \frac{3}{4} \div \frac{5}{3} \right)^5$

• (4/3div3/5)^5

• (5/3div4/3)^3

• (3/5div3/4)^3

Q 15 | Page 24

For any two non-zero rational numbers a and b, a4 ÷ b4 is equal to

• (a ÷ b)1

•  (a ÷ b)0

• (a ÷ b)4

• (a ÷ b)8

Q 16 | Page 24

For any two rational numbers a and b, a5 × b5 is equal to

•  (a × b)0

• (a × b)10

• (a × b)5

•  (a × b)25

Q 17 | Page 24

For a non-zero rational number a, a7 ÷ a12 is equal to

•  a5

• a−19

• a−5

• a19

Q 18 | Page 24

For a non zero rational number a, (a3)−2 is equal to

•  a9

• a−6

• a−9

• a1

## Chapter 2: Powers

Ex. 2.1Ex. 2.2Ex. 2.3Others ## RD Sharma solutions for Class 8 Maths chapter 2 - Powers

RD Sharma solutions for Class 8 Maths chapter 2 (Powers) 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 Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 2 Powers are Powers with Negative Exponents, Laws of Exponents, Use of Exponents to Express Small Numbers in Standard Form, Comparing Very Large and Very Small Numbers.

Using RD Sharma Class 8 solutions Powers 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 8 prefer RD Sharma Textbook Solutions to score more in exam.

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