Algebra Examples

${(\sqrt{\frac{x^{6}}{4}})}^{3}$

Step 1

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 2

Rewrite $4$ as $2^{2}$ .

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

Step 3

Rewrite $\frac{{(x^{3})}^{2}}{2^{2}}$ as ${(\frac{x^{3}}{2})}^{2}$ .

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

Step 4

Pull terms out from under the radical, assuming positive real numbers.

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

Step 5

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

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

Step 6

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

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Step 6.1

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

$\frac{x^{3 \cdot 3}}{2^{3}}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{x^{9}}{2^{3}}$

Step 7

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

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