Simplify ( cube root of x^4* square root of x^5)^-2

${(\sqrt[3]{x^{4}} \cdot \sqrt{x^{5}})}^{- 2}$

Factor out $x^{3}$ .

${(\sqrt[3]{x^{3} x} \cdot \sqrt{x^{5}})}^{- 2}$

Pull terms out from under the radical.

${(x \sqrt[3]{x} \cdot \sqrt{x^{5}})}^{- 2}$

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

Factor out $x^{4}$ .

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

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Pull terms out from under the radical.

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

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

${(x^{2} x^{1} \sqrt[3]{x} \cdot \sqrt{x})}^{- 2}$

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

${(x^{2 + 1} \sqrt[3]{x} \cdot \sqrt{x})}^{- 2}$

Add $2$ and $1$ .

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

Multiply $x^{3} \sqrt[3]{x} \sqrt{x}$ .

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{3} (x^{\frac{1}{2}} \sqrt[3]{x}))}^{- 2}$

Rewrite $x^{\frac{1}{2}}$ as $x^{\frac{3}{6}}$ .

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

Rewrite $x^{\frac{3}{6}}$ as $\sqrt[6]{x^{3}}$ .

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

${(x^{3} (\sqrt[6]{x^{3}} x^{\frac{1}{3}}))}^{- 2}$

Rewrite $x^{\frac{1}{3}}$ as $x^{\frac{2}{6}}$ .

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

Rewrite $x^{\frac{2}{6}}$ as $\sqrt[6]{x^{2}}$ .

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

Combine using the product rule for radicals.

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

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

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

${(x^{3} \sqrt[6]{x^{3 + 2}})}^{- 2}$

Add $3$ and $2$ .

${(x^{3} \sqrt[6]{x^{5}})}^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(x^{3} \sqrt[6]{x^{5}})}^{2}}$

Simplify the denominator.

Apply the product rule to $x^{3} \sqrt[6]{x^{5}}$ .

$\frac{1}{{(x^{3})}^{2} {\sqrt[6]{x^{5}}}^{2}}$

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

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

$\frac{1}{x^{3 \cdot 2} {\sqrt[6]{x^{5}}}^{2}}$

Multiply $3$ by $2$ .

$\frac{1}{x^{6} {\sqrt[6]{x^{5}}}^{2}}$

Rewrite ${\sqrt[6]{x^{5}}}^{2}$ as ${({(x^{5})}^{2})}^{\frac{1}{6}}$ .

$\frac{1}{x^{6} \sqrt[6]{{(x^{5})}^{2}}}$

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$\frac{1}{x^{6} \sqrt[6]{x^{5 \cdot 2}}}$

Multiply $5$ by $2$ .

$\frac{1}{x^{6} \sqrt[6]{x^{10}}}$

Factor out $x^{6}$ .

$\frac{1}{x^{6} \sqrt[6]{x^{6} x^{4}}}$

Pull terms out from under the radical.

$\frac{1}{x^{6} (x \sqrt[6]{x^{4}})}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{1}{x^{6} (x \sqrt[6]{{(x^{2})}^{2}})}$

Rewrite $\sqrt[6]{{(x^{2})}^{2}}$ as $\sqrt[3]{\sqrt{{(x^{2})}^{2}}}$ .

$\frac{1}{x^{6} (x \sqrt[3]{\sqrt{{(x^{2})}^{2}}})}$

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

$\frac{1}{x^{6} x \sqrt[3]{x^{2}}}$

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

Multiply $x^{6}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{1}{x^{6} x^{1} \sqrt[3]{x^{2}}}$

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

$\frac{1}{x^{6 + 1} \sqrt[3]{x^{2}}}$

Add $6$ and $1$ .

$\frac{1}{x^{7} \sqrt[3]{x^{2}}}$

Multiply $\frac{1}{x^{7} \sqrt[3]{x^{2}}}$ by $\frac{{\sqrt[3]{x^{2}}}^{2}}{{\sqrt[3]{x^{2}}}^{2}}$ .

$\frac{1}{x^{7} \sqrt[3]{x^{2}}} \cdot \frac{{\sqrt[3]{x^{2}}}^{2}}{{\sqrt[3]{x^{2}}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{1}{x^{7} \sqrt[3]{x^{2}}}$ by $\frac{{\sqrt[3]{x^{2}}}^{2}}{{\sqrt[3]{x^{2}}}^{2}}$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} \sqrt[3]{x^{2}} {\sqrt[3]{x^{2}}}^{2}}$

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} (\sqrt[3]{x^{2}} {\sqrt[3]{x^{2}}}^{2})}$

Raise $\sqrt[3]{x^{2}}$ to the power of $1$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} ({\sqrt[3]{x^{2}}}^{1} {\sqrt[3]{x^{2}}}^{2})}$

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} {\sqrt[3]{x^{2}}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} {\sqrt[3]{x^{2}}}^{3}}$

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} {(x^{\frac{2}{3}})}^{3}}$

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{2}{3} \cdot 3}}$

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{2 \cdot 3}{3}}}$

Multiply $2$ by $3$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{6}{3}}}$

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

Factor $3$ out of $6$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{3 \cdot 2}{3}}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{3 \cdot 2}{3 (1)}}}$

Cancel the common factor.

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{3 \cdot 2}{3 \cdot 1}}}$

Rewrite the expression.

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{\frac{2}{1}}}$

Divide $2$ by $1$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7} x^{2}}$

Multiply $x^{7}$ by $x^{2}$ by adding the exponents.

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

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{7 + 2}}$

Add $7$ and $2$ .

$\frac{{\sqrt[3]{x^{2}}}^{2}}{x^{9}}$

Simplify the numerator.

Rewrite ${\sqrt[3]{x^{2}}}^{2}$ as ${({(x^{2})}^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{{(x^{2})}^{2}}}{x^{9}}$

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

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

$\frac{\sqrt[3]{x^{2 \cdot 2}}}{x^{9}}$

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{x^{4}}}{x^{9}}$

Factor out $x^{3}$ .

$\frac{\sqrt[3]{x^{3} x}}{x^{9}}$

Pull terms out from under the radical.

$\frac{x \sqrt[3]{x}}{x^{9}}$

Cancel the common factor of $x$ and $x^{9}$ .

Factor $x$ out of $x \sqrt[3]{x}$ .

$\frac{x (\sqrt[3]{x})}{x^{9}}$

Cancel the common factors.

Factor $x$ out of $x^{9}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ( cube root of x^4* square root of x^5)^-2

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