Algebra Examples

$\sqrt[4]{\sqrt{h^{6} i^{24} j^{18}}}$

Step 1

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

$\sqrt[4]{\sqrt{h^{6} {(i^{4})}^{6} j^{18}}}$

Step 2

Rewrite $i^{4}$ as $1$ .

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Step 2.1

Rewrite $i^{4}$ as ${(i^{2})}^{2}$ .

$\sqrt[4]{\sqrt{h^{6} {({(i^{2})}^{2})}^{6} j^{18}}}$

Step 2.2

Rewrite $i^{2}$ as $- 1$ .

$\sqrt[4]{\sqrt{h^{6} {({(- 1)}^{2})}^{6} j^{18}}}$

Step 2.3

Raise $- 1$ to the power of $2$ .

$\sqrt[4]{\sqrt{h^{6} \cdot 1^{6} j^{18}}}$

Step 3

Simplify the expression.

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Step 3.1

One to any power is one.

$\sqrt[4]{\sqrt{h^{6} \cdot 1 j^{18}}}$

Step 3.2

Multiply $h^{6}$ by $1$ .

$\sqrt[4]{\sqrt{h^{6} j^{18}}}$

Step 4

Rewrite $h^{6} j^{18}$ as ${(h^{3} j^{9})}^{2}$ .

$\sqrt[4]{\sqrt{{(h^{3} j^{9})}^{2}}}$

Step 5

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

$\sqrt[4]{h^{3} j^{9}}$

Step 6

Rewrite $h^{3} j^{9}$ as ${(j^{2})}^{4} (h^{3} j)$ .

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Step 6.1

Factor out $j^{8}$ .

$\sqrt[4]{h^{3} (j^{8} j)}$

Step 6.2

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

$\sqrt[4]{h^{3} ({(j^{2})}^{4} j)}$

Step 6.3

Reorder $h^{3}$ and ${(j^{2})}^{4}$ .

$\sqrt[4]{{(j^{2})}^{4} h^{3} j}$

Step 6.4

Add parentheses.

$\sqrt[4]{{(j^{2})}^{4} (h^{3} j)}$

Step 7

Pull terms out from under the radical.

$j^{2} \sqrt[4]{h^{3} j}$