Algebra Examples

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

Step 1

Apply the product rule to $x \sqrt{x}$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

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

Step 2.4.2

Rewrite the expression.

$x^{2} x^{1}$

Step 2.5

Simplify.

$x^{2} x$

Step 3

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

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Step 3.1

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

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Step 3.1.1

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

$x^{2} x^{1}$

Step 3.1.2

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

$x^{2 + 1}$

Step 3.2

Add $2$ and $1$ .

$x^{3}$