Simplify ((x^3y)/(z^4))^6

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

Step 1

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

Apply the product rule to $\frac{x^{3} y}{z^{4}}$ .

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

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

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

Step 2

Multiply the exponents in ${(x^{3})}^{6}$ .

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

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

Multiply $3$ by $6$ .

$\frac{x^{18} y^{6}}{{(z^{4})}^{6}}$

Step 3

Multiply the exponents in ${(z^{4})}^{6}$ .

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

$\frac{x^{18} y^{6}}{z^{4 \cdot 6}}$

Multiply $4$ by $6$ .

$\frac{x^{18} y^{6}}{z^{24}}$