Simplify the Radical Expression 5 fourth root of 112c^24d^13

$5 \sqrt[4]{112 c^{24} d^{13}}$

Step 1

Rewrite $112 c^{24} d^{13}$ as ${(2 c^{6} d^{3})}^{4} \cdot (7 d)$ .

Factor $16$ out of $112$ .

$5 \sqrt[4]{16 (7) c^{24} d^{13}}$

Rewrite $16$ as $2^{4}$ .

$5 \sqrt[4]{2^{4} \cdot 7 c^{24} d^{13}}$

Rewrite $c^{24}$ as ${(c^{6})}^{4}$ .

$5 \sqrt[4]{2^{4} \cdot 7 {(c^{6})}^{4} d^{13}}$

Factor out $d^{12}$ .

$5 \sqrt[4]{2^{4} \cdot 7 {(c^{6})}^{4} (d^{12} d)}$

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

$5 \sqrt[4]{2^{4} \cdot 7 {(c^{6})}^{4} ({(d^{3})}^{4} d)}$

Move $7$ .

$5 \sqrt[4]{2^{4} {(c^{6})}^{4} {(d^{3})}^{4} \cdot 7 d}$

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

$5 \sqrt[4]{{(2 c^{6} d^{3})}^{4} \cdot 7 d}$

Add parentheses.

$5 \sqrt[4]{{(2 c^{6} d^{3})}^{4} \cdot (7 d)}$

Step 2

Pull terms out from under the radical.

$5 (| 2 c^{6} d^{3} | \sqrt[4]{7 d})$

Step 3

Remove non-negative terms from the absolute value.

$5 (2 c^{6} | d^{3} | \sqrt[4]{7 d})$

Step 4

Multiply $2$ by $5$ .

$10 c^{6} | d^{3} | \sqrt[4]{7 d}$