Algebra Examples

${(\sqrt{5 x^{3}})}^{2}$

Step 1

Rewrite $5 x^{3}$ as $x^{2} \cdot (5 x)$ .

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Step 1.1

Factor out $x^{2}$ .

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

Step 1.2

Reorder $5$ and $x^{2}$ .

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

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Apply the product rule to $x \sqrt{5 x}$ .

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

Step 4

Rewrite ${\sqrt{5 x}}^{2}$ as $5 x$ .

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x}$ as ${(5 x)}^{\frac{1}{2}}$ .

$x^{2} {({(5 x)}^{\frac{1}{2}})}^{2}$

Step 4.2

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

$x^{2} {(5 x)}^{\frac{1}{2} \cdot 2}$

Step 4.3

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

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

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

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

Step 4.4.2

Rewrite the expression.

$x^{2} {(5 x)}^{1}$

Step 4.5

Simplify.

$x^{2} (5 x)$

Step 5

Rewrite using the commutative property of multiplication.

$5 x^{2} x$

Step 6

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

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Step 6.1

Move $x$ .

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

Step 6.2

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

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Step 6.2.1

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

$5 (x^{1} x^{2})$

Step 6.2.2

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

$5 x^{1 + 2}$

Step 6.3

Add $1$ and $2$ .

$5 x^{3}$