Simplify (4(ya^-5)^-1)/(4y^-8a^4)

$\frac{4 {(y a^{- 5})}^{- 1}}{4 y^{- 8} a^{4}}$

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

$\frac{4}{4 y^{- 8} a^{4} (y a^{- 5})}$

Simplify the denominator.

Multiply $y^{- 8}$ by $y$ by adding the exponents.

Move $y$ .

$\frac{4}{4 (y \cdot y^{- 8}) a^{4} a^{- 5}}$

Multiply $y$ by $y^{- 8}$ .

Raise $y$ to the power of $1$ .

$\frac{4}{4 (y^{1} y^{- 8}) a^{4} a^{- 5}}$

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

$\frac{4}{4 y^{1 - 8} a^{4} a^{- 5}}$

Subtract $8$ from $1$ .

$\frac{4}{4 y^{- 7} a^{4} a^{- 5}}$

Multiply $a^{4}$ by $a^{- 5}$ by adding the exponents.

Move $a^{- 5}$ .

$\frac{4}{4 y^{- 7} (a^{- 5} a^{4})}$

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

$\frac{4}{4 y^{- 7} a^{- 5 + 4}}$

Add $- 5$ and $4$ .

$\frac{4}{4 y^{- 7} a^{- 1}}$

Simplify the expression.

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

$\frac{4 y^{7}}{4 a^{- 1}}$

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

$\frac{4 y^{7} a}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y^{7} a}{4}$

Divide $y^{7} a$ by $1$ .

$y^{7} a$