Laws of Exponents - Numbers with Exponent Zero, One, Negative Exponents

a° = 1.

a¹ = a.

a^{- m} = `1/a^m`

1. Numbers with exponent zero:

Any number (except 0) raised to the power (or exponent) 0 is 1.

Consider following examples,

7³ ÷ 7³ = 7^{3 - 3} = 7°.

And `7^3/7^3 = (7 × 7 × 7)/(7 × 7 × 7) = 1`

Therefore, 7° = 1

Similarly,

a³ ÷ a³ = `a^3/a^3 = (a × a × a)/(a × a × a) = 1`

Thus, a° = 1.....(for any non-zero integer a).

Examples,

(i) 2°+ 3° + 4° = 1 + 1 + 1 = 3

(ii) 2° × 3° × 4° = 1 × 1 × 1 = 1

(iii) (3° + 2°) × 5° = (1 + 1) × 1 = 2

2. Numbers with Exponent One:

Any number with one as the exponent is equal to the number itself.

a¹ = a

Example,

(i) 9¹ = 9.

(ii) 6¹ = 6.

(iii) 4¹ = 4.

3. Power with a Negative Exponent:

Negative exponents can be converted into positive exponents.

a^{- m} = `1/a^m`

Example,

(i) 9¹ = `1/9^-1`.

(ii) 6^{- 3} = `1/6^3`.

(iii) 4^{- 7} = `1/4^7`.