Algebra Examples

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

Step 1

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

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Step 1.1

Apply the product rule to $\frac{2 x^{4}}{3}$ .

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

Step 1.2

Apply the product rule to $2 x^{4}$ .

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

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{8 {(x^{4})}^{3}}{3^{3}}$

Step 2.2

Multiply the exponents in ${(x^{4})}^{3}$ .

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Step 2.2.1

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

$\frac{8 x^{4 \cdot 3}}{3^{3}}$

Step 2.2.2

Multiply $4$ by $3$ .

$\frac{8 x^{12}}{3^{3}}$

Step 3

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

$\frac{8 x^{12}}{27}$