Algebra Examples

$x \sqrt{x^{5}}$

Step 1

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

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Step 1.1

Factor out $x^{4}$ .

$x \sqrt{x^{4} x}$

Step 1.2

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

$x \sqrt{{(x^{2})}^{2} x}$

Step 2

Pull terms out from under the radical.

$x (| x^{2} | \sqrt{x})$

Step 3

Remove non-negative terms from the absolute value.

$x (x^{2} \sqrt{x})$

Step 4

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 4.1

Move $x^{2}$ .

$x^{2} x \sqrt{x}$

Step 4.2

Multiply $x^{2}$ by $x$ .

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Step 4.2.1

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

$x^{2} x^{1} \sqrt{x}$

Step 4.2.2

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

$x^{2 + 1} \sqrt{x}$

Step 4.3

Add $2$ and $1$ .

$x^{3} \sqrt{x}$