Laws of indices - EdexcelDividing indices

Simplify \(b^5 \div b^3\).

\(b^5 \div b^3\) can be written as \(\frac{b^5}{b^3}\) and writing out the denominator and numerator in full gives \(\frac{b \times b \times b \times b \times b}{b \times b \times b}\). 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 \(b^2\).