Simplify the Radical Expression ( square root of w^11)/( cube root of w^8)

$\frac{\sqrt{w^{11}}}{\sqrt[3]{w^{8}}}$

Simplify the numerator.

Rewrite $w^{11}$ as ${(w^{5})}^{2} w$ .

Factor out $w^{10}$ .

$\frac{\sqrt{w^{10} w}}{\sqrt[3]{w^{8}}}$

Rewrite $w^{10}$ as ${(w^{5})}^{2}$ .

$\frac{\sqrt{{(w^{5})}^{2} w}}{\sqrt[3]{w^{8}}}$

Pull terms out from under the radical.

$\frac{| w^{5} | \sqrt{w}}{\sqrt[3]{w^{8}}}$

Simplify the denominator.

Rewrite $w^{8}$ as ${(w^{2})}^{3} w^{2}$ .

Factor out $w^{6}$ .

$\frac{| w^{5} | \sqrt{w}}{\sqrt[3]{w^{6} w^{2}}}$

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

$\frac{| w^{5} | \sqrt{w}}{\sqrt[3]{{(w^{2})}^{3} w^{2}}}$

Pull terms out from under the radical.

$\frac{| w^{5} | \sqrt{w}}{w^{2} \sqrt[3]{w^{2}}}$

Multiply $\frac{| w^{5} | \sqrt{w}}{w^{2} \sqrt[3]{w^{2}}}$ by $\frac{{\sqrt[3]{w^{2}}}^{2}}{{\sqrt[3]{w^{2}}}^{2}}$ .

$\frac{| w^{5} | \sqrt{w}}{w^{2} \sqrt[3]{w^{2}}} \cdot \frac{{\sqrt[3]{w^{2}}}^{2}}{{\sqrt[3]{w^{2}}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{| w^{5} | \sqrt{w}}{w^{2} \sqrt[3]{w^{2}}}$ by $\frac{{\sqrt[3]{w^{2}}}^{2}}{{\sqrt[3]{w^{2}}}^{2}}$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} \sqrt[3]{w^{2}} {\sqrt[3]{w^{2}}}^{2}}$

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} (\sqrt[3]{w^{2}} {\sqrt[3]{w^{2}}}^{2})}$

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} ({\sqrt[3]{w^{2}}}^{1} {\sqrt[3]{w^{2}}}^{2})}$

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} {\sqrt[3]{w^{2}}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} {\sqrt[3]{w^{2}}}^{3}}$

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

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} {(w^{\frac{2}{3}})}^{3}}$

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{2}{3} \cdot 3}}$

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{2 \cdot 3}{3}}}$

Multiply $2$ by $3$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{6}{3}}}$

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

Factor $3$ out of $6$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{3 \cdot 2}{3}}}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{3 \cdot 2}{3 (1)}}}$

Cancel the common factor.

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{3 \cdot 2}{3 \cdot 1}}}$

Rewrite the expression.

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{\frac{2}{1}}}$

Divide $2$ by $1$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2} w^{2}}$

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

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

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{2 + 2}}$

Add $2$ and $2$ .

$\frac{| w^{5} | \sqrt{w} {\sqrt[3]{w^{2}}}^{2}}{w^{4}}$

Simplify the numerator.

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

$\frac{| w^{5} | \sqrt{w} \sqrt[3]{{(w^{2})}^{2}}}{w^{4}}$

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

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

$\frac{| w^{5} | \sqrt{w} \sqrt[3]{w^{2 \cdot 2}}}{w^{4}}$

Multiply $2$ by $2$ .

$\frac{| w^{5} | \sqrt{w} \sqrt[3]{w^{4}}}{w^{4}}$

Factor out $w^{3}$ .

$\frac{| w^{5} | \sqrt{w} \sqrt[3]{w^{3} w}}{w^{4}}$

Pull terms out from under the radical.

$\frac{| w^{5} | \sqrt{w} w \sqrt[3]{w}}{w^{4}}$

Combine exponents.

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

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

$\frac{| w^{5} | w (w^{\frac{1}{2}} \sqrt[3]{w})}{w^{4}}$

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

$\frac{| w^{5} | w (w^{\frac{3}{6}} \sqrt[3]{w})}{w^{4}}$

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

$\frac{| w^{5} | w (\sqrt[6]{w^{3}} \sqrt[3]{w})}{w^{4}}$

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

$\frac{| w^{5} | w (\sqrt[6]{w^{3}} w^{\frac{1}{3}})}{w^{4}}$

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

$\frac{| w^{5} | w (\sqrt[6]{w^{3}} w^{\frac{2}{6}})}{w^{4}}$

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

$\frac{| w^{5} | w (\sqrt[6]{w^{3}} \sqrt[6]{w^{2}})}{w^{4}}$

Combine using the product rule for radicals.

$\frac{| w^{5} | w \sqrt[6]{w^{3} w^{2}}}{w^{4}}$

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

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

$\frac{| w^{5} | w \sqrt[6]{w^{3 + 2}}}{w^{4}}$

Add $3$ and $2$ .

$\frac{| w^{5} | w \sqrt[6]{w^{5}}}{w^{4}}$

Cancel the common factor of $w$ and $w^{4}$ .

Factor $w$ out of $| w^{5} | w \sqrt[6]{w^{5}}$ .

$\frac{w (| w^{5} | \sqrt[6]{w^{5}})}{w^{4}}$

Cancel the common factors.

Factor $w$ out of $w^{4}$ .

$\frac{w (| w^{5} | \sqrt[6]{w^{5}})}{w \cdot w^{3}}$

Cancel the common factor.

$\frac{w (| w^{5} | \sqrt[6]{w^{5}})}{w \cdot w^{3}}$

Rewrite the expression.

$\frac{| w^{5} | \sqrt[6]{w^{5}}}{w^{3}}$

Simplify the Radical Expression ( square root of w^11)/( cube root of w^8)

Related Questions

Support LCMGCF.com by disabling your adblocker.