Algebra Examples

$3 x \sqrt{\frac{x^{5}}{81}}$

Step 1

Rewrite $\frac{x^{5}}{81}$ as ${(\frac{x^{2}}{9})}^{2} x$ .

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Step 1.1

Factor the perfect power ${(x^{2})}^{2}$ out of $x^{5}$ .

$3 x \sqrt{\frac{{(x^{2})}^{2} x}{81}}$

Step 1.2

Factor the perfect power $9^{2}$ out of $81$ .

$3 x \sqrt{\frac{{(x^{2})}^{2} x}{9^{2} \cdot 1}}$

Step 1.3

Rearrange the fraction $\frac{{(x^{2})}^{2} x}{9^{2} \cdot 1}$ .

$3 x \sqrt{{(\frac{x^{2}}{9})}^{2} x}$

Step 2

Pull terms out from under the radical.

$3 x (\frac{x^{2}}{9} \sqrt{x})$

Step 3

Combine $\frac{x^{2}}{9}$ and $\sqrt{x}$ .

$3 x \frac{x^{2} \sqrt{x}}{9}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $3 x$ .

$3 (x) \frac{x^{2} \sqrt{x}}{9}$

Step 4.2

Factor $3$ out of $9$ .

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

Step 4.3

Cancel the common factor.

$3 x \frac{x^{2} \sqrt{x}}{3 \cdot 3}$

Step 4.4

Rewrite the expression.

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

Step 5

Combine $x$ and $\frac{x^{2} \sqrt{x}}{3}$ .

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

Step 6

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

$\frac{x^{2} x^{1} \sqrt{x}}{3}$

Step 7

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

$\frac{x^{2 + 1} \sqrt{x}}{3}$

Step 8

Add $2$ and $1$ .

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