Simplify (8x^-2)/(4y^-5)

$\frac{8 x^{- 2}}{4 y^{- 5}}$

Step 1

Simplify.

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{8}{4 y^{- 5} x^{2}}$

Move $y^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{8 y^{5}}{4 x^{2}}$

Step 2

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 y^{5}$ .

$\frac{4 (2 y^{5})}{4 x^{2}}$

Cancel the common factors.

Factor $4$ out of $4 x^{2}$ .

$\frac{4 (2 y^{5})}{4 (x^{2})}$

Cancel the common factor.

$\frac{4 (2 y^{5})}{4 x^{2}}$

Rewrite the expression.

$\frac{2 y^{5}}{x^{2}}$