# Solution of Chapter 2. Powers (RD Sharma - Mathematics Book)

## Exercise 2.1

1

Express each of the following as a rational number of the form , where p and q are integers and q 0:

(i) 2-3

(ii) (-4)-2

(iii) (iv) (v) 2

Find the values of each of the following:

(i) (ii) (iii) (iv) 3

Find the values of each of the following:

(i) (ii) (iii) (iv) 4

Simplify:

(i) (ii) (iii) (iv) 5

Simplify:

(i) (ii) (iii) (iv) 6

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

7

By what number should be multiplied so that the product may be equal to ?

8

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

## Exercise 2.2

1

Write each of the following in exponential form:

(i) (ii) 2

Evaluate:

(i) 5-2

(ii) (-3)-2

(iii) (iv) 3

Express each of the following as a rational number in the form :

(i) 6-1

(ii) (-7)-1

(iii) (iv) (v) 4

Simplify:

(i) (ii) (iii) (iv) (v) 5

Express each of the following rational numbers with a negative exponent:

(i) (ii) 35

(iii) (iv) (v) 6

Express each of the following rational numbers with a positive exponent:

(i) (ii) (iii) (iv) (v) 7

Simplify:

(i) (ii) (iii) (iv) (v) 8

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

9

By what number should be multiplied so that the product may be equal to ?

10

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

11

By what number should be multiplied so that the product may be ?

12

Find x, if

(i) (ii) (iii) (iv) (v) (vi) 13

If x= , find the value of x-2.

13

If x = , find the value of x-1.

14

Find the value of x for which .

## Exercise 2.3

1

Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.00000000000942

(iii) 0.00000000085

(iv) (v) (vi) 0.00072984

(vii) 0.000437 (viii) 2

Write the following numbers in the usual form:

(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) 