Simplify z(y^-5z^7)^-1y^-5

$z {(y^{- 5} z^{7})}^{- 1} y^{- 5}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$z {(\frac{1}{y^{5}} z^{7})}^{- 1} y^{- 5}$

Step 2

Combine $\frac{1}{y^{5}}$ and $z^{7}$ .

$z {(\frac{z^{7}}{y^{5}})}^{- 1} y^{- 5}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$z \frac{y^{5}}{z^{7}} y^{- 5}$

Step 4

Cancel the common factor of $z$ .

Factor $z$ out of $z^{7}$ .

$z \frac{y^{5}}{z \cdot z^{6}} y^{- 5}$

Cancel the common factor.

$z \frac{y^{5}}{z \cdot z^{6}} y^{- 5}$

Rewrite the expression.

$\frac{y^{5}}{z^{6}} y^{- 5}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{5}}{z^{6}} \cdot \frac{1}{y^{5}}$

Step 6

Combine.

$\frac{y^{5} \cdot 1}{z^{6} y^{5}}$

Step 7

Cancel the common factor of $y^{5}$ .

Cancel the common factor.

$\frac{y^{5} \cdot 1}{z^{6} y^{5}}$

Rewrite the expression.

$\frac{1}{z^{6}}$