Simplify cube root of (b^3)/( square root of b^3)

$\sqrt[3]{\frac{b^{3}}{\sqrt[2]{b^{3}}}}$

Simplify the denominator.

Factor out $b^{2}$ .

$\sqrt[3]{\frac{b^{3}}{\sqrt{b^{2} b}}}$

Pull terms out from under the radical.

$\sqrt[3]{\frac{b^{3}}{b \sqrt{b}}}$

Cancel the common factor of $b^{3}$ and $b$ .

Factor $b$ out of $b^{3}$ .

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

Cancel the common factors.

Factor $b$ out of $b \sqrt{b}$ .

$\sqrt[3]{\frac{b \cdot b^{2}}{b (\sqrt{b})}}$

Cancel the common factor.

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

Rewrite the expression.

$\sqrt[3]{\frac{b^{2}}{\sqrt{b}}}$

Multiply $\frac{b^{2}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

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

Combine and simplify the denominator.

Multiply $\frac{b^{2}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$\sqrt[3]{\frac{b^{2} \sqrt{b}}{\sqrt{b} \sqrt{b}}}$

Raise $\sqrt{b}$ to the power of $1$ .

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

Raise $\sqrt{b}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

$\sqrt[3]{\frac{b^{2} \sqrt{b}}{{\sqrt{b}}^{2}}}$

Rewrite ${\sqrt{b}}^{2}$ as $b$ .

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

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

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

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

Combine $\frac{1}{2}$ and $2$ .

$\sqrt[3]{\frac{b^{2} \sqrt{b}}{b^{\frac{2}{2}}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\sqrt[3]{\frac{b^{2} \sqrt{b}}{b^{\frac{2}{2}}}}$

Rewrite the expression.

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

Simplify.

$\sqrt[3]{\frac{b^{2} \sqrt{b}}{b}}$

Cancel the common factor of $b^{2}$ and $b$ .

Factor $b$ out of $b^{2} \sqrt{b}$ .

$\sqrt[3]{\frac{b (b \sqrt{b})}{b}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{b (b \sqrt{b})}{b^{1}}}$

Factor $b$ out of $b^{1}$ .

$\sqrt[3]{\frac{b (b \sqrt{b})}{b \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{b (b \sqrt{b})}{b \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{b \sqrt{b}}{1}}$

Divide $b \sqrt{b}$ by $1$ .

$\sqrt[3]{b \sqrt{b}}$

Simplify cube root of (b^3)/( square root of b^3)

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