Algebra Examples

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

Step 1

Factor out $x^{2}$ .

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

Step 2

Pull terms out from under the radical.

$\sqrt{x} \cdot (x \sqrt{x})$

Step 3

Multiply $\sqrt{x} (x \sqrt{x})$ .

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Step 3.1

Raise $\sqrt{x}$ to the power of $1$ .

$x ({\sqrt{x}}^{1} \sqrt{x})$

Step 3.2

Raise $\sqrt{x}$ to the power of $1$ .

$x ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

Step 3.3

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

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

Step 3.4

Add $1$ and $1$ .

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

Step 4

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$x {(x^{\frac{1}{2}})}^{2}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x \cdot x^{\frac{1}{2} \cdot 2}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$x \cdot x^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$x \cdot x^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$x \cdot x^{1}$

Step 4.5

Simplify.

$x \cdot x$

Step 5

Multiply $x$ by $x$ .

$x^{2}$