Simplify (x^-7)/(8y^2)*8/(x^8y^-2)

$\frac{x^{- 7}}{8 y^{2}} \cdot \frac{8}{x^{8} y^{- 2}}$

Combine.

$\frac{x^{- 7} \cdot 8}{8 y^{2} (x^{8} y^{- 2})}$

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

Move $y^{- 2}$ .

$\frac{x^{- 7} \cdot 8}{8 (y^{- 2} y^{2}) x^{8}}$

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

$\frac{x^{- 7} \cdot 8}{8 y^{- 2 + 2} x^{8}}$

Add $- 2$ and $2$ .

$\frac{x^{- 7} \cdot 8}{8 y^{0} x^{8}}$

Simplify $8 y^{0} x^{8}$ .

$\frac{x^{- 7} \cdot 8}{8 x^{8}}$

Move $x^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{8}{8 x^{8} x^{7}}$

Multiply $x^{8}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{8}{8 (x^{7} x^{8})}$

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

$\frac{8}{8 x^{7 + 8}}$

Add $7$ and $8$ .

$\frac{8}{8 x^{15}}$

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{8 x^{15}}$

Rewrite the expression.

$\frac{1}{x^{15}}$