Simplify (2x^3yz^2)^-2

${(2 x^{3} y z^{2})}^{- 2}$

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

$\frac{1}{{(2 x^{3} y z^{2})}^{2}}$

Simplify the denominator.

Apply the product rule to $2 x^{3} y z^{2}$ .

$\frac{1}{{(2 x^{3} y)}^{2} {(z^{2})}^{2}}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 x^{3} y$ .

$\frac{1}{{(2 x^{3})}^{2} y^{2} {(z^{2})}^{2}}$

Apply the product rule to $2 x^{3}$ .

$\frac{1}{2^{2} {(x^{3})}^{2} y^{2} {(z^{2})}^{2}}$

Raise $2$ to the power of $2$ .

$\frac{1}{4 {(x^{3})}^{2} y^{2} {(z^{2})}^{2}}$

Multiply the exponents in ${(x^{3})}^{2}$ .

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

$\frac{1}{4 x^{3 \cdot 2} y^{2} {(z^{2})}^{2}}$

Multiply $3$ by $2$ .

$\frac{1}{4 x^{6} y^{2} {(z^{2})}^{2}}$

Multiply the exponents in ${(z^{2})}^{2}$ .

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

$\frac{1}{4 x^{6} y^{2} z^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{1}{4 x^{6} y^{2} z^{4}}$