Question

fully simplify using only positive exponents. $\frac{5xy}{5x^{2}y^{8}}$

Explanation:

Step1: Cancel out the common factor 5

$\frac{5xy}{5x^{2}y^{8}}=\frac{xy}{x^{2}y^{8}}$

Step2: Use the quotient - rule of exponents $a^m\div a^n=a^{m - n}$ for $x$ and $y$ terms

For $x$: $\frac{x}{x^{2}}=x^{1-2}=x^{-1}=\frac{1}{x}$; for $y$: $\frac{y}{y^{8}}=y^{1 - 8}=y^{-7}=\frac{1}{y^{7}}$
So, $\frac{xy}{x^{2}y^{8}}=\frac{1}{xy^{7}}$

Answer:

$\frac{1}{xy^{7}}$