Exercise 2.3 - Powers RD Sharma Solutions | Mathematics (Maths) Class 8 PDF Download

Q.1. Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.00000000000943

(iii) 0.00000000085

(iv) 846 × 10⁷

(v) 3759 × 10⁻⁴

(vi) 0.00072984

(vii) 0.000437 × 10⁴

(viii) 4 ÷ 100000

Ans: To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point.

(i) 6020000000000000 = 6.02 x 10¹⁵(The decimal point is moved 15 places to the left.)

(ii) 0.0000000000943 = 9.43 x 10⁻¹²(The decimal point is moved 12 places to the right.)

(iii) 0.00000000085 = 8.5 x 10−¹⁰(The decimal point is moved 10 places to the right.)

(iv) 846 x 10⁷ = 8.46 x 10² x 10⁷ = 8.46 x 10⁹ (The decimal point is moved two places to the left.)

(v) 3759 x 10⁻⁴ = 3.759 x 10³ x 10⁻⁴ = 3.759 x 10⁻¹(The decimal point is moved three places to the left.)

(vi) 0.00072984 = 7.984 x 10⁻⁴(The decimal point is moved four places to the right.)

(vii) 0.000437 x 10⁴ = 4.37 x 10⁻⁴ x 10⁴ = 4.37 x 100 = 4.37(The decimal point is moved four places to the right.)

(viii) 4/100000 = 4 x 100000⁻¹ = 4 x 10⁻⁵(Just count the number of zeros in 1,00,000 to determine the exponent of 10.)

Q.2. Write the following numbers in the usual form:

(i) 4.83 × 10⁷

(ii) 3.02 × 10⁻⁶

(iii) 4.5 × 10⁴

(iv) 3 × 10⁻⁸

(v) 1.0001 × 10⁹

(vi) 5.8 × 10²

(vii) 3.61492 × 10⁶

(viii) 3.25 × 10⁻⁷

Ans:

(i) 4.83 x 10⁷ = 4.83 x 1,00,00,000 = 4,83,00,000

(ii) 3.02 x 10⁻⁶ = 3.02/106 = 3.02/10,00,000 = 0.00000302

(iii) 4.5 x 10⁴ = 4.5 x 10,000 = 45,000

(iv) 3 x 10⁻⁸ = 3/108 = 3/10,00,00,000 = 0.00000003

(v) 1.0001 x 10⁹ = 1.0001 x 1,00,00,00,000 = 1,00,01,00,000

(vi) 5.8 x 10² = 5.8 x 100 = 580

(vii)  3.61492 x 10⁶ = 3.61492 x 10,00,000 = 3614920

(viii) 3.25 x 10⁻⁷ = 3.25/107 = 3.25/1,00,00,000 = 0.000000325

Exercise (MCQs)

Q.1. Square ofis

(a) −2/3

(b) 2/3

(c) −4/9

(d) 4/9

Ans: (d) 4/9

To square a number is to raise it to the power of 2. Hence, the square of (−2/3) is

Q.2. Cube ofis

(a) 1/8

(b) 1/16

(c) −1/8

(d) −1/16

Ans: (c) -1/8

The cube of a number is the number raised to the power of 3. Hence the cube of −1/2 is

Q.3. Which of the following is not equal to?

(a)

(b)

(c)

(d)

Ans: 

(c)  −(3⁴/5⁴)

= =

It is not equal to −

Q.4. Which  of the following is not reciprocal of (2/3)4?

(a)

(b)

(c)

(d)

Ans: 

(c) (3/2)⁻⁴

The reciprocal of is

Therefore, option (a) is the correct answer.

Option (b) is just re-expressing the number with a negative exponent.

Option (d) is obtained by working out the exponent.

Hence,option (c) is not the reciprocal of

Q.5. Which of the following numbers is not equal to −8/27?

(a)

(b)

(c)

(d)

Ans:

(a) (2/3)^-3

We can writeas. It can be written in the forms given below.

 ---> work out the minuses 

Hence, option (b) is equal to

We can also write:

Hence, option (c) is also equal to

We can also write:

Hence, option (d) is also equal to −8/27.

This leaves out option (a) as the one not equal to.

Q.6. is equal to

(a)

(b)

(c)

(d)

Ans: 

(b) 

Rearrange (2/3)⁻⁵ to get a positive exponent.

Q.7. is equal to

(a)

(b)

(c)

(d)

Ans: 

(a) (−1/2)⁸

=

=

Q.8. is equal to

(a)

(b)

(c)

(d)

Ans: 

(c) (−5)⁵

We have:

=

=

=

=

=

Q.9.  is equal to

(a) 4/25

(b) −4/25

(c) (−2/5)¹²

(d) 25/4

Ans: 

(a) 4/25

We have:

=

=

=

Q.10.  is equal to

a) (1/3)⁶

(b) (1/3)⁸

(c) (1/3)²⁴

(d) (1/3)¹⁶

Ans:

(b) (1/3)⁸

We have:

=

Q.11. is equal to

(a) 0

(b) 1/5

(c) 1

(d) 5

Ans: 

(c) 1

We have:

 --> (a⁰ = 1, for every non-zero rational number a.)

Q.12.  is equal to

(a) 2/3

(b) −2/3

(c) 3/2

(d) none of these

Ans:

We have:

Q.13. is equal to

(a)

(b)

(c)

(d)

Ans:

We have:

Q.14. is equal to

Ans: 

(a) 

We have;

Q.15. For any two non-zero rational numbers a and b, a4 ÷ b4 is equal to

(a) (a ÷ b)¹

(b) (a ÷ b)⁰

(c) (a ÷ b)⁴

(d) (a ÷ b)⁸

Ans: 

This is one of the basic exponential formulae, i.e.

Q.16. For any two rational numbers a and b, a5 × b5 is equal to

(a) (a × b)⁰

(b) (a × b)¹⁰

(c) (a × b)⁵

(d) (a × b)²⁵

Ans: 

(c) (a x b)⁵

aⁿ x bⁿ = (a x b)ⁿ

Hence,

a⁵ x b⁵ = (a x b)⁵

Q.17. For a non-zero rational number a, a7 ÷ a12 is equal to

(a) a⁵

(b) a⁻¹⁹

(c) a⁻⁵

(d) a¹⁹

Ans: 

(c) a−5

Hence,

Q.18. For a non zero rational number a, (a3)−2 is equal to

(a) a⁹

(b) a⁻⁶

(c) a⁻⁹

(d) a¹

Ans: 

(b) a⁻⁶

= a^-6