Simplify (c^3)/( fourth root of d^7)

$\frac{c^{3}}{\sqrt[4]{d^{7}}}$

Simplify the denominator.

Factor out $d^{4}$ .

$\frac{c^{3}}{\sqrt[4]{d^{4} d^{3}}}$

Pull terms out from under the radical.

$\frac{c^{3}}{d \sqrt[4]{d^{3}}}$

Multiply $\frac{c^{3}}{d \sqrt[4]{d^{3}}}$ by $\frac{{\sqrt[4]{d^{3}}}^{3}}{{\sqrt[4]{d^{3}}}^{3}}$ .

$\frac{c^{3}}{d \sqrt[4]{d^{3}}} \cdot \frac{{\sqrt[4]{d^{3}}}^{3}}{{\sqrt[4]{d^{3}}}^{3}}$

Combine and simplify the denominator.

Multiply $\frac{c^{3}}{d \sqrt[4]{d^{3}}}$ by $\frac{{\sqrt[4]{d^{3}}}^{3}}{{\sqrt[4]{d^{3}}}^{3}}$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \sqrt[4]{d^{3}} {\sqrt[4]{d^{3}}}^{3}}$

Move $\sqrt[4]{d^{3}}$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d (\sqrt[4]{d^{3}} {\sqrt[4]{d^{3}}}^{3})}$

Raise $\sqrt[4]{d^{3}}$ to the power of $1$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d ({\sqrt[4]{d^{3}}}^{1} {\sqrt[4]{d^{3}}}^{3})}$

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

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d {\sqrt[4]{d^{3}}}^{1 + 3}}$

Add $1$ and $3$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d {\sqrt[4]{d^{3}}}^{4}}$

Rewrite ${\sqrt[4]{d^{3}}}^{4}$ as $d^{3}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{d^{3}}$ as $d^{\frac{3}{4}}$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d {(d^{\frac{3}{4}})}^{4}}$

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

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{3}{4} \cdot 4}}$

Combine $\frac{3}{4}$ and $4$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{3 \cdot 4}{4}}}$

Multiply $3$ by $4$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{12}{4}}}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{4 \cdot 3}{4}}}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{4 \cdot 3}{4 (1)}}}$

Cancel the common factor.

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{4 \cdot 3}{4 \cdot 1}}}$

Rewrite the expression.

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{\frac{3}{1}}}$

Divide $3$ by $1$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d \cdot d^{3}}$

Multiply $d$ by $d^{3}$ by adding the exponents.

Multiply $d$ by $d^{3}$ .

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

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d^{1} d^{3}}$

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

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d^{1 + 3}}$

Add $1$ and $3$ .

$\frac{c^{3} {\sqrt[4]{d^{3}}}^{3}}{d^{4}}$

Simplify the numerator.

Rewrite ${\sqrt[4]{d^{3}}}^{3}$ as ${({(d^{3})}^{3})}^{\frac{1}{4}}$ .

$\frac{c^{3} \sqrt[4]{{(d^{3})}^{3}}}{d^{4}}$

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

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

$\frac{c^{3} \sqrt[4]{d^{3 \cdot 3}}}{d^{4}}$

Multiply $3$ by $3$ .

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

Rewrite $d^{9}$ as ${(d^{2})}^{4} d$ .

Factor out $d^{8}$ .

$\frac{c^{3} \sqrt[4]{d^{8} d}}{d^{4}}$

Rewrite $d^{8}$ as ${(d^{2})}^{4}$ .

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

Pull terms out from under the radical.

$\frac{c^{3} d^{2} \sqrt[4]{d}}{d^{4}}$

Cancel the common factor of $d^{2}$ and $d^{4}$ .

Factor $d^{2}$ out of $c^{3} d^{2} \sqrt[4]{d}$ .

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

Cancel the common factors.

Factor $d^{2}$ out of $d^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{c^{3} \sqrt[4]{d}}{d^{2}}$

Simplify (c^3)/( fourth root of d^7)

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