Algebra Examples

$\sqrt[4]{k^{5} \cdot k}$

Step 1

Multiply $k^{5}$ by $k$ by adding the exponents.

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Step 1.1

Multiply $k^{5}$ by $k$ .

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Step 1.1.1

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

$\sqrt[4]{k^{5} k^{1}}$

Step 1.1.2

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

$\sqrt[4]{k^{5 + 1}}$

Step 1.2

Add $5$ and $1$ .

$\sqrt[4]{k^{6}}$

Step 2

Factor out $k^{4}$ .

$\sqrt[4]{k^{4} k^{2}}$

Step 3

Pull terms out from under the radical.

$k \sqrt[4]{k^{2}}$

Step 4

Rewrite $\sqrt[4]{k^{2}}$ as $\sqrt{\sqrt{k^{2}}}$ .

$k \sqrt{\sqrt{k^{2}}}$

Step 5

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

$k \sqrt{k}$