Algebra Examples

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

Step 1

Apply the product rule to $a^{6} b^{\frac{1}{2}}$ .

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

Step 2

Multiply the exponents in ${(a^{6})}^{6}$ .

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Step 2.1

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

$a^{6 \cdot 6} {(b^{\frac{1}{2}})}^{6} \sqrt[6]{b^{6}}$

Step 2.2

Multiply $6$ by $6$ .

$a^{36} {(b^{\frac{1}{2}})}^{6} \sqrt[6]{b^{6}}$

Step 3

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

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Step 3.1

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

$a^{36} b^{\frac{1}{2} \cdot 6} \sqrt[6]{b^{6}}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $6$ .

$a^{36} b^{\frac{1}{2} \cdot (2 (3))} \sqrt[6]{b^{6}}$

Step 3.2.2

Cancel the common factor.

$a^{36} b^{\frac{1}{2} \cdot (2 \cdot 3)} \sqrt[6]{b^{6}}$

Step 3.2.3

Rewrite the expression.

$a^{36} b^{3} \sqrt[6]{b^{6}}$

Step 4

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

$a^{36} b^{3} b$

Step 5

Multiply $b^{3}$ by $b$ by adding the exponents.

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Step 5.1

Move $b$ .

$a^{36} (b \cdot b^{3})$

Step 5.2

Multiply $b$ by $b^{3}$ .

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Step 5.2.1

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

$a^{36} (b^{1} b^{3})$

Step 5.2.2

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

$a^{36} b^{1 + 3}$

Step 5.3

Add $1$ and $3$ .

$a^{36} b^{4}$