Pre-Algebra Examples

$(\sqrt{x^{4}}) (\sqrt{x^{5}})$

Step 1

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

$\sqrt{{(x^{2})}^{2}} \sqrt{x^{5}}$

Step 2

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

$x^{2} \sqrt{x^{5}}$

Step 3

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

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Step 3.1

Factor out $x^{4}$ .

$x^{2} \sqrt{x^{4} x}$

Step 3.2

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Move $x^{2}$ .

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

Step 5.2

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

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

Step 5.3

Add $2$ and $2$ .

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