Simplify (7x^5y^6)/(28x^15y^-2)

$\frac{7 x^{5} y^{6}}{28 x^{15} y^{- 2}}$

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

$\frac{7 x^{5} y^{6} y^{2}}{28 x^{15}}$

Multiply $y^{6}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{7 x^{5} (y^{2} y^{6})}{28 x^{15}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 x^{5} y^{2 + 6}}{28 x^{15}}$

Add $2$ and $6$ .

$\frac{7 x^{5} y^{8}}{28 x^{15}}$

Cancel the common factor of $7$ and $28$ .

Factor $7$ out of $7 x^{5} y^{8}$ .

$\frac{7 (x^{5} y^{8})}{28 x^{15}}$

Cancel the common factors.

Factor $7$ out of $28 x^{15}$ .

$\frac{7 (x^{5} y^{8})}{7 (4 x^{15})}$

Cancel the common factor.

$\frac{7 (x^{5} y^{8})}{7 (4 x^{15})}$

Rewrite the expression.

$\frac{x^{5} y^{8}}{4 x^{15}}$

Cancel the common factor of $x^{5}$ and $x^{15}$ .

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

$\frac{x^{5} (y^{8})}{4 x^{15}}$

Cancel the common factors.

Factor $x^{5}$ out of $4 x^{15}$ .

$\frac{x^{5} (y^{8})}{x^{5} (4 x^{10})}$

Cancel the common factor.

$\frac{x^{5} y^{8}}{x^{5} (4 x^{10})}$

Rewrite the expression.

$\frac{y^{8}}{4 x^{10}}$