Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Rewrite using the commutative property of multiplication.

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

Step 1.2

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

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

Step 1.3

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

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

Move $x^{6}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Add $6$ and $3$ .

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