Simplify cube root of (25d^15)/(8c^7)

$\sqrt[3]{\frac{25 d^{15}}{8 c^{7}}}$

Step 1

Rewrite $\frac{25 d^{15}}{8 c^{7}}$ as ${(\frac{d^{5}}{2 c^{2}})}^{3} \frac{25}{c}$ .

Factor the perfect power ${(d^{5})}^{3}$ out of $25 d^{15}$ .

$\sqrt[3]{\frac{{(d^{5})}^{3} \cdot 25}{8 c^{7}}}$

Factor the perfect power ${(2 c^{2})}^{3}$ out of $8 c^{7}$ .

$\sqrt[3]{\frac{{(d^{5})}^{3} \cdot 25}{{(2 c^{2})}^{3} c}}$

Rearrange the fraction $\frac{{(d^{5})}^{3} \cdot 25}{{(2 c^{2})}^{3} c}$ .

$\sqrt[3]{{(\frac{d^{5}}{2 c^{2}})}^{3} \frac{25}{c}}$

Step 2

Pull terms out from under the radical.

$\frac{d^{5}}{2 c^{2}} \sqrt[3]{\frac{25}{c}}$

Step 3

Rewrite $\sqrt[3]{\frac{25}{c}}$ as $\frac{\sqrt[3]{25}}{\sqrt[3]{c}}$ .

$\frac{d^{5}}{2 c^{2}} \cdot \frac{\sqrt[3]{25}}{\sqrt[3]{c}}$

Step 4

Combine.

$\frac{d^{5} \sqrt[3]{25}}{2 c^{2} \sqrt[3]{c}}$

Step 5

Multiply $\frac{d^{5} \sqrt[3]{25}}{2 c^{2} \sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

$\frac{d^{5} \sqrt[3]{25}}{2 c^{2} \sqrt[3]{c}} \cdot \frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$

Step 6

Combine and simplify the denominator.

Multiply $\frac{d^{5} \sqrt[3]{25}}{2 c^{2} \sqrt[3]{c}}$ by $\frac{{\sqrt[3]{c}}^{2}}{{\sqrt[3]{c}}^{2}}$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} \sqrt[3]{c} {\sqrt[3]{c}}^{2}}$

Move $\sqrt[3]{c}$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} (\sqrt[3]{c} {\sqrt[3]{c}}^{2})}$

Raise $\sqrt[3]{c}$ to the power of $1$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} ({\sqrt[3]{c}}^{1} {\sqrt[3]{c}}^{2})}$

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

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} {\sqrt[3]{c}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} {\sqrt[3]{c}}^{3}}$

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

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

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} {(c^{\frac{1}{3}})}^{3}}$

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

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} c^{\frac{1}{3} \cdot 3}}$

Combine $\frac{1}{3}$ and $3$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} c^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} c^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} c^{1}}$

Simplify.

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{2} c}$

Step 7

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

Move $c$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 (c \cdot c^{2})}$

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

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

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 (c^{1} c^{2})}$

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

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{1 + 2}}$

Add $1$ and $2$ .

$\frac{d^{5} \sqrt[3]{25} {\sqrt[3]{c}}^{2}}{2 c^{3}}$

Step 8

Simplify the numerator.

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

$\frac{d^{5} \sqrt[3]{25} \sqrt[3]{c^{2}}}{2 c^{3}}$

Combine using the product rule for radicals.

$\frac{d^{5} \sqrt[3]{c^{2} \cdot 25}}{2 c^{3}}$

Step 9

Move $25$ to the left of $c^{2}$ .

$\frac{d^{5} \sqrt[3]{25 c^{2}}}{2 c^{3}}$

Simplify cube root of (25d^15)/(8c^7)

Related Questions

Support LCMGCF.com by disabling your adblocker.