Question

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

Explanation:

Step1: Cancel the common factor 5

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

Step2: Use the quotient rule for exponents ($\frac{a^{m}}{a^{n}} = a^{m - n}$) for x

$\frac{xy}{x^{2}y^{8}}=\frac{x^{1-2}y}{y^{8}}$

Step3: Simplify the exponent of x

$\frac{x^{1 - 2}y}{y^{8}}=\frac{x^{-1}y}{y^{8}}$

Step4: Use the quotient rule for exponents for y

$\frac{x^{-1}y}{y^{8}}=x^{-1}y^{1 - 8}$

Step5: Simplify the exponent of y

$x^{-1}y^{1 - 8}=x^{-1}y^{-7}$

Step6: Rewrite negative exponents as positive ( $a^{-n}=\frac{1}{a^{n}}$ )

$x^{-1}y^{-7}=\frac{1}{x y^{7}}$

Answer:

$\frac{1}{x y^{7}}$