Simplify cube root of (((x^2)^3)^4)/(x^10x^-6x^4)

$\sqrt[3]{\frac{{({(x^{2})}^{3})}^{4}}{x^{10} x^{- 6} x^{4}}}$

Step 1

Multiply $x^{10}$ by $x^{- 6}$ by adding the exponents.

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

$\sqrt[3]{\frac{{({(x^{2})}^{3})}^{4}}{x^{10 - 6} x^{4}}}$

Subtract $6$ from $10$ .

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

Step 2

Multiply $x^{4}$ by $x^{4}$ by adding the exponents.

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

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

Add $4$ and $4$ .

$\sqrt[3]{\frac{{({(x^{2})}^{3})}^{4}}{x^{8}}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${({(x^{2})}^{3})}^{4}$ .

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

$\sqrt[3]{\frac{{(x^{2})}^{3 \cdot 4}}{x^{8}}}$

Multiply $3$ by $4$ .

$\sqrt[3]{\frac{{(x^{2})}^{12}}{x^{8}}}$

Multiply the exponents in ${(x^{2})}^{12}$ .

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

$\sqrt[3]{\frac{x^{2 \cdot 12}}{x^{8}}}$

Multiply $2$ by $12$ .

$\sqrt[3]{\frac{x^{24}}{x^{8}}}$

Step 4

Cancel the common factor of $x^{24}$ and $x^{8}$ .

Factor $x^{8}$ out of $x^{24}$ .

$\sqrt[3]{\frac{x^{8} x^{16}}{x^{8}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{8} x^{16}}{x^{8} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{8} x^{16}}{x^{8} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{x^{16}}{1}}$

Divide $x^{16}$ by $1$ .

$\sqrt[3]{x^{16}}$

Step 5

Rewrite $x^{16}$ as ${(x^{5})}^{3} x$ .

Factor out $x^{15}$ .

$\sqrt[3]{x^{15} x}$

Rewrite $x^{15}$ as ${(x^{5})}^{3}$ .

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

Step 6

Pull terms out from under the radical.

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

Simplify cube root of (((x^2)^3)^4)/(x^10x^-6x^4)

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