PROPERTIES OF EXPONENTS

In this section, we will learn the properties of exponents. We have listed the properties of exponents.

x^m ⋅ xⁿ = x^{(m + n)}	If two or more terms are multiplying with the same base, we may write only one base and add the powers.
x^m / xⁿ = x^{(m – n)}	If two terms are dividing with the same base, we may write only one base and subtract the powers.
(x^m)ⁿ = x^mn	If we have power raised to another power, then we should multiply both the powers
x^-m = 1/x^m (or) (a/b)^-m = (b/a)^m	If we have negative exponent, then we can write the reciprocal form of the given number to make the negative exponent as positive.
x⁰ = 1	The value of anything to the power will be 1

Example problems on properties of exponents

Example 1 :

Simplify

2m² ⋅ 3m³

Solution :

2m² ⋅ 3m³ = 6m^{(2 + 3)}

2m² ⋅ 3m³ = 6m⁵

Example 2 :

Simplify

Solution :

(2x³/y³) ⋅ (x⁴/ y²) = 2x^{(3 + 4)} / y^{(3 + 2)}

= 2x⁷ / y⁵

Example 3 :

Simplify

Solution :

= 4g^-4 b⁴ ⋅ 2gb^-5

= 8g^{(-4 + 1)} b^{(4 – 5)}

= 8g^-3 b^{– 1}

= 8/g³b

Example 4 :

Simplify

Solution :

For all the terms, we have same base. So, we can write only one base and add the powers.

= (6/7)^{(4 + 2 + 3)}

= (6/7)⁹