Simplify ( square root of 5x^3)^2

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

Step 1

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

Factor out $x^{2}$ .

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

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

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

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 $5 x$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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.

Move $x$ .

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

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

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

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

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

$5 x^{1 + 2}$

Add $1$ and $2$ .

$5 x^{3}$