Basic Math Examples

${(a^{2} b^{6})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $a^{2} b^{6}$ .

${(a^{2})}^{\frac{1}{2}} {(b^{6})}^{\frac{1}{2}}$

Step 2

Multiply the exponents in ${(a^{2})}^{\frac{1}{2}}$ .

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Step 2.1

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

$a^{2 (\frac{1}{2})} {(b^{6})}^{\frac{1}{2}}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

$a^{2 (\frac{1}{2})} {(b^{6})}^{\frac{1}{2}}$

Step 2.2.2

Rewrite the expression.

$a^{1} {(b^{6})}^{\frac{1}{2}}$

Step 3

Simplify.

$a {(b^{6})}^{\frac{1}{2}}$

Step 4

Multiply the exponents in ${(b^{6})}^{\frac{1}{2}}$ .

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Step 4.1

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

$a b^{6 (\frac{1}{2})}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $6$ .

$a b^{2 (3) \frac{1}{2}}$

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$a b^{3}$