Evaluate ((3x)/2)^4

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

Step 1

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

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

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

Apply the product rule to $3 x$ .

$\frac{3^{4} x^{4}}{2^{4}}$

Step 2

Raise $3$ to the power of $4$ .

$\frac{81 x^{4}}{2^{4}}$

Step 3

Raise $2$ to the power of $4$ .

$\frac{81 x^{4}}{16}$