Simplify (z^-2zy^(3/5))^8

${(z^{- 2} \cdot z \cdot y^{\frac{3}{5}})}^{8}$

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

Multiply $z^{- 2}$ by $z$ .

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

${(z^{- 2} \cdot z^{1} \cdot y^{\frac{3}{5}})}^{8}$

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

${(z^{- 2 + 1} \cdot y^{\frac{3}{5}})}^{8}$

Add $- 2$ and $1$ .

${(z^{- 1} \cdot y^{\frac{3}{5}})}^{8}$

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

${(\frac{1}{z} \cdot y^{\frac{3}{5}})}^{8}$

Combine $\frac{1}{z}$ and $y^{\frac{3}{5}}$ .

${(\frac{y^{\frac{3}{5}}}{z})}^{8}$

Apply basic rules of exponents.

Apply the product rule to $\frac{y^{\frac{3}{5}}}{z}$ .

$\frac{{(y^{\frac{3}{5}})}^{8}}{z^{8}}$

Multiply the exponents in ${(y^{\frac{3}{5}})}^{8}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{\frac{3}{5} \cdot 8}}{z^{8}}$

Multiply $\frac{3}{5} \cdot 8$ .

Combine $\frac{3}{5}$ and $8$ .

$\frac{y^{\frac{3 \cdot 8}{5}}}{z^{8}}$

Multiply $3$ by $8$ .

$\frac{y^{\frac{24}{5}}}{z^{8}}$

Simplify (z^-2*z*y^(3/5))^8