Algebra Examples

${(\frac{6 a b^{0}}{2 a^{4} b})}^{3}$

Step 1

Move $b^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{6 a}{2 a^{4} b \cdot b^{0}})}^{3}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $b$ by $b^{0}$ by adding the exponents.

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Step 2.1.1

Move $b^{0}$ .

${(\frac{6 a}{2 a^{4} (b^{0} b)})}^{3}$

Step 2.1.2

Multiply $b^{0}$ by $b$ .

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Step 2.1.2.1

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

${(\frac{6 a}{2 a^{4} (b^{0} b^{1})})}^{3}$

Step 2.1.2.2

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

${(\frac{6 a}{2 a^{4} b^{0 + 1}})}^{3}$

Step 2.1.3

Add $0$ and $1$ .

${(\frac{6 a}{2 a^{4} b^{1}})}^{3}$

Step 2.2

Simplify $2 a^{4} b^{1}$ .

${(\frac{6 a}{2 a^{4} b})}^{3}$

Step 3

Cancel the common factor of $6$ and $2$ .

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Step 3.1

Factor $2$ out of $6 a$ .

${(\frac{2 (3 a)}{2 a^{4} b})}^{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 a^{4} b$ .

${(\frac{2 (3 a)}{2 (a^{4} b)})}^{3}$

Step 3.2.2

Cancel the common factor.

${(\frac{2 (3 a)}{2 (a^{4} b)})}^{3}$

Step 3.2.3

Rewrite the expression.

${(\frac{3 a}{a^{4} b})}^{3}$

Step 4

Cancel the common factor of $a$ and $a^{4}$ .

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Step 4.1

Factor $a$ out of $3 a$ .

${(\frac{a \cdot 3}{a^{4} b})}^{3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $a^{4} b$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{3}{a^{3} b}$ .

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

Step 5.2

Apply the product rule to $a^{3} b$ .

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

Step 6

Raise $3$ to the power of $3$ .

$\frac{27}{{(a^{3})}^{3} b^{3}}$

Step 7

Multiply the exponents in ${(a^{3})}^{3}$ .

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Step 7.1

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

$\frac{27}{a^{3 \cdot 3} b^{3}}$

Step 7.2

Multiply $3$ by $3$ .

$\frac{27}{a^{9} b^{3}}$