Simplify ((x^4y^2)/(z^-4))^-3

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

Step 1

Move $z^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{4} y^{2} z^{4})}^{- 3}$

Step 2

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

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

Step 3

Simplify the denominator.

Apply the product rule to $x^{4} y^{2} z^{4}$ .

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

Apply the product rule to $x^{4} y^{2}$ .

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

Multiply the exponents in ${(x^{4})}^{3}$ .

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

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

Multiply $4$ by $3$ .

$\frac{1}{x^{12} {(y^{2})}^{3} {(z^{4})}^{3}}$

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

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

$\frac{1}{x^{12} y^{2 \cdot 3} {(z^{4})}^{3}}$

Multiply $2$ by $3$ .

$\frac{1}{x^{12} y^{6} {(z^{4})}^{3}}$

Multiply the exponents in ${(z^{4})}^{3}$ .

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

$\frac{1}{x^{12} y^{6} z^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{1}{x^{12} y^{6} z^{12}}$