Finite Math Examples

$\frac{\sqrt[3]{6 c^{4} d^{14}}}{\sqrt[3]{48 c^{- 2} d^{2}}}$

Step 1

Combine $\sqrt[3]{6 c^{4} d^{14}}$ and $\sqrt[3]{48 c^{- 2} d^{2}}$ into a single radical.

$\sqrt[3]{\frac{6 c^{4} d^{14}}{48 c^{- 2} d^{2}}}$

Step 2

Reduce the expression $\frac{6 c^{4} d^{14}}{48 c^{- 2} d^{2}}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $6$ out of $6 c^{4} d^{14}$ .

$\sqrt[3]{\frac{6 (c^{4} d^{14})}{48 c^{- 2} d^{2}}}$

Step 2.2

Factor $6$ out of $48 c^{- 2} d^{2}$ .

$\sqrt[3]{\frac{6 (c^{4} d^{14})}{6 (8 c^{- 2} d^{2})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{6 (c^{4} d^{14})}{6 (8 c^{- 2} d^{2})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{c^{4} d^{14}}{8 c^{- 2} d^{2}}}$

Step 3

Move $c^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[3]{\frac{c^{4} d^{14} c^{2}}{8 d^{2}}}$

Step 4

Multiply $c^{4}$ by $c^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $c^{2}$ .

$\sqrt[3]{\frac{c^{2} c^{4} d^{14}}{8 d^{2}}}$

Step 4.2

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

$\sqrt[3]{\frac{c^{2 + 4} d^{14}}{8 d^{2}}}$

Step 4.3

Add $2$ and $4$ .

$\sqrt[3]{\frac{c^{6} d^{14}}{8 d^{2}}}$

Step 5

Cancel the common factor of $d^{14}$ and $d^{2}$ .

Tap for more steps...

Step 5.1

Factor $d^{2}$ out of $c^{6} d^{14}$ .

$\sqrt[3]{\frac{d^{2} (c^{6} d^{12})}{8 d^{2}}}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $d^{2}$ out of $8 d^{2}$ .

$\sqrt[3]{\frac{d^{2} (c^{6} d^{12})}{d^{2} \cdot 8}}$

Step 5.2.2

Cancel the common factor.

$\sqrt[3]{\frac{d^{2} (c^{6} d^{12})}{d^{2} \cdot 8}}$

Step 5.2.3

Rewrite the expression.

$\sqrt[3]{\frac{c^{6} d^{12}}{8}}$

Step 6

Rewrite $c^{6} d^{12}$ as ${(c^{2} d^{4})}^{3}$ .

$\sqrt[3]{\frac{{(c^{2} d^{4})}^{3}}{8}}$

Step 7

Rewrite $8$ as $2^{3}$ .

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

Step 8

Rewrite $\frac{{(c^{2} d^{4})}^{3}}{2^{3}}$ as ${(\frac{c^{2} d^{4}}{2})}^{3}$ .

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

Step 9

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

$\frac{c^{2} d^{4}}{2}$