Pre-Algebra Examples

$\sqrt[15]{m^{10} n^{15} x^{20}}$

Step 1

Rewrite $m^{10} n^{15} x^{20}$ as ${(n x)}^{15} (m^{10} x^{5})$ .

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Step 1.1

Factor out $x^{15}$ .

$\sqrt[15]{m^{10} n^{15} (x^{15} x^{5})}$

Step 1.2

Move $m^{10}$ .

$\sqrt[15]{n^{15} x^{15} m^{10} x^{5}}$

Step 1.3

Rewrite $n^{15} x^{15}$ as ${(n x)}^{15}$ .

$\sqrt[15]{{(n x)}^{15} m^{10} x^{5}}$

Step 1.4

Add parentheses.

$\sqrt[15]{{(n x)}^{15} (m^{10} x^{5})}$

Step 2

Pull terms out from under the radical.

$n x \sqrt[15]{m^{10} x^{5}}$

Step 3

Rewrite $m^{10} x^{5}$ as ${(m^{2} x)}^{5}$ .

$n x \sqrt[15]{{(m^{2} x)}^{5}}$

Step 4

Rewrite $\sqrt[15]{{(m^{2} x)}^{5}}$ as $\sqrt[3]{\sqrt[5]{{(m^{2} x)}^{5}}}$ .

$n x \sqrt[3]{\sqrt[5]{{(m^{2} x)}^{5}}}$

Step 5

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

$n x \sqrt[3]{m^{2} x}$