Law of indices – division

Example

Simplify b^5 \div b^3.

b^5 \div b^3 can be written as \frac{b^5}{b^3}

b^5 \div b^3

b^5 = b \times b \times b \times b \times b and b^3 = b \times b \times b

b^5 \div b^3 so \frac{b^5}{b^3} = \frac{b \times b \times b \times b \times b}{b \times b \times b}

There are common factors of b in the numerator and denominator and these can be cancelled out, giving \frac{\cancel{b} \times \cancel{b} \times \cancel{b} \times b \times b}{\cancel{b} \times \cancel{b} \times \cancel{b}} which leaves b \times b = b^2.

This means b^5 \div b^3 can be simplified to b^2.

curriculum-key-fact
a^m \div a^n = a^(m – n)