Evaluate (1/2c^3d)^5

${(\frac{1}{2} c^{3} d)}^{5}$

Step 1

Multiply $\frac{1}{2} (c^{3} d)$ .

Combine $c^{3}$ and $\frac{1}{2}$ .

${(\frac{c^{3}}{2} d)}^{5}$

Combine $\frac{c^{3}}{2}$ and $d$ .

${(\frac{c^{3} d}{2})}^{5}$

Step 2

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

Apply the product rule to $\frac{c^{3} d}{2}$ .

$\frac{{(c^{3} d)}^{5}}{2^{5}}$

Apply the product rule to $c^{3} d$ .

$\frac{{(c^{3})}^{5} d^{5}}{2^{5}}$

Step 3

Multiply the exponents in ${(c^{3})}^{5}$ .

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

$\frac{c^{3 \cdot 5} d^{5}}{2^{5}}$

Multiply $3$ by $5$ .

$\frac{c^{15} d^{5}}{2^{5}}$

Step 4

Raise $2$ to the power of $5$ .

$\frac{c^{15} d^{5}}{32}$