Pre-Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Factor out $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Tap for more steps...

Step 3.1

Factor out $x^{4}$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

Tap for more steps...

Step 5.1

Move $x^{2}$ .

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

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$x^{2} x^{1} \sqrt{5 x} \sqrt{5 x}$

Step 5.2.2

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

$x^{2 + 1} \sqrt{5 x} \sqrt{5 x}$

Step 5.3

Add $2$ and $1$ .

$x^{3} \sqrt{5 x} \sqrt{5 x}$

Step 6

Multiply $x^{3} \sqrt{5 x} \sqrt{5 x}$ .

Tap for more steps...

Step 6.1

Raise $\sqrt{5 x}$ to the power of $1$ .

$x^{3} ({\sqrt{5 x}}^{1} \sqrt{5 x})$

Step 6.2

Raise $\sqrt{5 x}$ to the power of $1$ .

$x^{3} ({\sqrt{5 x}}^{1} {\sqrt{5 x}}^{1})$

Step 6.3

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

$x^{3} {\sqrt{5 x}}^{1 + 1}$

Step 6.4

Add $1$ and $1$ .

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

Step 7

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

Tap for more steps...

Step 7.1

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

$x^{3} {({(5 x)}^{\frac{1}{2}})}^{2}$

Step 7.2

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

$x^{3} {(5 x)}^{\frac{1}{2} \cdot 2}$

Step 7.3

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

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

Step 7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.4.1

Cancel the common factor.

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

Step 7.4.2

Rewrite the expression.

$x^{3} {(5 x)}^{1}$

Step 7.5

Simplify.

$x^{3} (5 x)$

Step 8

Rewrite using the commutative property of multiplication.

$5 x^{3} x$

Step 9

Multiply $x^{3}$ by $x$ by adding the exponents.

Tap for more steps...

Step 9.1

Move $x$ .

$5 (x \cdot x^{3})$

Step 9.2

Multiply $x$ by $x^{3}$ .

Tap for more steps...

Step 9.2.1

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

$5 (x^{1} x^{3})$

Step 9.2.2

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

$5 x^{1 + 3}$

Step 9.3

Add $1$ and $3$ .

$5 x^{4}$