Basic Math Examples

${(\sqrt[6]{b})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{b}$ as $b^{\frac{1}{6}}$ .

${(b^{\frac{1}{6}})}^{3}$

Step 2

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

$b^{\frac{1}{6} \cdot 3}$

Step 3

Combine $\frac{1}{6}$ and $3$ .

$b^{\frac{3}{6}}$

Step 4

Cancel the common factor of $3$ and $6$ .

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Step 4.1

Factor $3$ out of $3$ .

$b^{\frac{3 (1)}{6}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $6$ .

$b^{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 4.2.2

Cancel the common factor.

$b^{\frac{3 \cdot 1}{3 \cdot 2}}$

Step 4.2.3

Rewrite the expression.

$b^{\frac{1}{2}}$

Step 5

Rewrite $b^{\frac{1}{2}}$ as $\sqrt{b}$ .

$\sqrt{b}$