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 \(b^2\).

\(\frac{a^3}{a} = a^{3-1} = a^2\)

Simplify \(\frac{6a^3b^5}{4ab^3}\)

\(\frac{6}{4} = \frac{3}{2}\)

\(\frac{a^3}{a} = a^{3-1} = a^2\)

\(\frac{b^5}{b^3} = b^{5-3} = b^2\)

So \(\frac{6a^3b^5}{4ab^3} = \frac{3a^2b^2}{2}\)