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

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Combine $z^{3}$ and $\frac{3}{4}$ .

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

Step 3

Move $3$ to the left of $z^{3}$ .

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

Step 4

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

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

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

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

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

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

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

Step 5

Simplify the expression.

Raise $- 1$ to the power of $2$ .

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

Multiply $\frac{3^{2} {(z^{3})}^{2}}{4^{2}}$ by $1$ .

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

Step 6

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 {(z^{3})}^{2}}{4^{2}}$

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

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

$\frac{9 z^{3 \cdot 2}}{4^{2}}$

Multiply $3$ by $2$ .

$\frac{9 z^{6}}{4^{2}}$

Step 7

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

$\frac{9 z^{6}}{16}$