Algebra Examples

$2 \sqrt{3 - x} \cdot 4 \sqrt[3]{3 - x}$

Step 1

Multiply $4$ by $2$ .

$8 \sqrt{3 - x} \sqrt[3]{3 - x}$

Step 2

Rewrite the expression using the least common index of $6$ .

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{3 - x}$ as ${(3 - x)}^{\frac{1}{3}}$ .

$8 ({(3 - x)}^{\frac{1}{3}} \sqrt{3 - x})$

Step 2.2

Rewrite ${(3 - x)}^{\frac{1}{3}}$ as ${(3 - x)}^{\frac{2}{6}}$ .

$8 ({(3 - x)}^{\frac{2}{6}} \sqrt{3 - x})$

Step 2.3

Rewrite ${(3 - x)}^{\frac{2}{6}}$ as $\sqrt[6]{{(3 - x)}^{2}}$ .

$8 (\sqrt[6]{{(3 - x)}^{2}} \sqrt{3 - x})$

Step 2.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 - x}$ as ${(3 - x)}^{\frac{1}{2}}$ .

$8 (\sqrt[6]{{(3 - x)}^{2}} {(3 - x)}^{\frac{1}{2}})$

Step 2.5

Rewrite ${(3 - x)}^{\frac{1}{2}}$ as ${(3 - x)}^{\frac{3}{6}}$ .

$8 (\sqrt[6]{{(3 - x)}^{2}} {(3 - x)}^{\frac{3}{6}})$

Step 2.6

Rewrite ${(3 - x)}^{\frac{3}{6}}$ as $\sqrt[6]{{(3 - x)}^{3}}$ .

$8 (\sqrt[6]{{(3 - x)}^{2}} \sqrt[6]{{(3 - x)}^{3}})$

Step 3

Combine using the product rule for radicals.

$8 \sqrt[6]{{(3 - x)}^{2} {(3 - x)}^{3}}$

Step 4

Multiply ${(3 - x)}^{2}$ by ${(3 - x)}^{3}$ by adding the exponents.

Tap for more steps...

Step 4.1

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

$8 \sqrt[6]{{(3 - x)}^{2 + 3}}$

Step 4.2

Add $2$ and $3$ .

$8 \sqrt[6]{{(3 - x)}^{5}}$