Algebra Examples

$\sqrt{81 x} \cdot \sqrt[4]{16 x^{10}}$

Step 1

Rewrite $81 x$ as ${(3^{2})}^{2} x$ .

Tap for more steps...

Step 1.1

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} x} \cdot \sqrt[4]{16 x^{10}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{{(3^{2})}^{2} x} \cdot \sqrt[4]{16 x^{10}}$

Step 2

Pull terms out from under the radical.

$3^{2} \sqrt{x} \cdot \sqrt[4]{16 x^{10}}$

Step 3

Raise $3$ to the power of $2$ .

$9 \sqrt{x} \cdot \sqrt[4]{16 x^{10}}$

Step 4

Rewrite $16 x^{10}$ as ${(2 x^{2})}^{4} x^{2}$ .

Tap for more steps...

Step 4.1

Rewrite $16$ as $2^{4}$ .

$9 \sqrt{x} \cdot \sqrt[4]{2^{4} x^{10}}$

Step 4.2

Factor out $x^{8}$ .

$9 \sqrt{x} \cdot \sqrt[4]{2^{4} (x^{8} x^{2})}$

Step 4.3

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$9 \sqrt{x} \cdot \sqrt[4]{2^{4} ({(x^{2})}^{4} x^{2})}$

Step 4.4

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

$9 \sqrt{x} \cdot \sqrt[4]{{(2 x^{2})}^{4} x^{2}}$

Step 5

Pull terms out from under the radical.

$9 \sqrt{x} \cdot (2 x^{2} \sqrt[4]{x^{2}})$

Step 6

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$9 \sqrt{x} \cdot (2 x^{2} \sqrt{\sqrt{x^{2}}})$

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$9 \sqrt{x} \cdot (2 x^{2} \sqrt{x})$

Step 8

Multiply $9 \sqrt{x} (2 x^{2} \sqrt{x})$ .

Tap for more steps...

Step 8.1

Multiply $2$ by $9$ .

$18 \sqrt{x} (x^{2} \sqrt{x})$

Step 8.2

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

$18 (x^{2} ({\sqrt{x}}^{1} \sqrt{x}))$

Step 8.3

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

$18 (x^{2} ({\sqrt{x}}^{1} {\sqrt{x}}^{1}))$

Step 8.4

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

$18 (x^{2} {\sqrt{x}}^{1 + 1})$

Step 8.5

Add $1$ and $1$ .

$18 (x^{2} {\sqrt{x}}^{2})$

Step 9

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

Tap for more steps...

Step 9.1

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

$18 (x^{2} {(x^{\frac{1}{2}})}^{2})$

Step 9.2

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

$18 (x^{2} x^{\frac{1}{2} \cdot 2})$

Step 9.3

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

$18 (x^{2} x^{\frac{2}{2}})$

Step 9.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 9.4.1

Cancel the common factor.

$18 (x^{2} x^{\frac{2}{2}})$

Step 9.4.2

Rewrite the expression.

$18 (x^{2} x^{1})$

Step 9.5

Simplify.

$18 (x^{2} x)$

Step 10

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

Tap for more steps...

Step 10.1

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

Tap for more steps...

Step 10.1.1

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

$18 (x^{2} x^{1})$

Step 10.1.2

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

$18 x^{2 + 1}$

Step 10.2

Add $2$ and $1$ .

$18 x^{3}$