Simplify (x/2)^3(5x^6)

${(\frac{x}{2})}^{3} (5 x^{6})$

Step 1

Simplify the expression.

Rewrite using the commutative property of multiplication.

$5 {(\frac{x}{2})}^{3} x^{6}$

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

$5 \frac{x^{3}}{2^{3}} x^{6}$

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

$5 \frac{x^{3}}{8} x^{6}$

Step 2

Combine $5$ and $\frac{x^{3}}{8}$ .

$\frac{5 x^{3}}{8} x^{6}$

Step 3

Multiply $\frac{5 x^{3}}{8} x^{6}$ .

Combine $\frac{5 x^{3}}{8}$ and $x^{6}$ .

$\frac{5 x^{3} x^{6}}{8}$

Multiply $x^{3}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$\frac{5 (x^{6} x^{3})}{8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 x^{6 + 3}}{8}$

Add $6$ and $3$ .

$\frac{5 x^{9}}{8}$