Simplify ( cube root of x^5)^3

${(\sqrt[3]{x^{5}})}^{3}$

Step 1

Factor out $x^{3}$ .

${\sqrt[3]{x^{3} x^{2}}}^{3}$

Step 2

Pull terms out from under the radical.

${(x \sqrt[3]{x^{2}})}^{3}$

Step 3

Apply the product rule to $x \sqrt[3]{x^{2}}$ .

$x^{3} {\sqrt[3]{x^{2}}}^{3}$

Step 4

Rewrite ${\sqrt[3]{x^{2}}}^{3}$ as $x^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

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

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

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

Combine $\frac{2}{3}$ and $3$ .

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

Multiply $2$ by $3$ .

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

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{3} x^{\frac{3 \cdot 2}{3 (1)}}$

Cancel the common factor.

$x^{3} x^{\frac{3 \cdot 2}{3 \cdot 1}}$

Rewrite the expression.

$x^{3} x^{\frac{2}{1}}$

Divide $2$ by $1$ .

$x^{3} x^{2}$

Step 5

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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

$x^{3 + 2}$

Add $3$ and $2$ .

$x^{5}$