Algebra Examples

${({(a^{\frac{1}{12}} b^{- 3})}^{3})}^{- 2}$

Step 1

Multiply the exponents in ${({(a^{\frac{1}{12}} b^{- 3})}^{3})}^{- 2}$ .

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Step 1.1

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

${(a^{\frac{1}{12}} b^{- 3})}^{3 \cdot - 2}$

Step 1.2

Multiply $3$ by $- 2$ .

${(a^{\frac{1}{12}} b^{- 3})}^{- 6}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(a^{\frac{1}{12}} \frac{1}{b^{3}})}^{- 6}$

Step 3

Combine $a^{\frac{1}{12}}$ and $\frac{1}{b^{3}}$ .

${(\frac{a^{\frac{1}{12}}}{b^{3}})}^{- 6}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{b^{3}}{a^{\frac{1}{12}}})}^{6}$

Step 5

Apply the product rule to $\frac{b^{3}}{a^{\frac{1}{12}}}$ .

$\frac{{(b^{3})}^{6}}{{(a^{\frac{1}{12}})}^{6}}$

Step 6

Multiply the exponents in ${(b^{3})}^{6}$ .

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Step 6.1

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

$\frac{b^{3 \cdot 6}}{{(a^{\frac{1}{12}})}^{6}}$

Step 6.2

Multiply $3$ by $6$ .

$\frac{b^{18}}{{(a^{\frac{1}{12}})}^{6}}$

Step 7

Multiply the exponents in ${(a^{\frac{1}{12}})}^{6}$ .

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Step 7.1

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

$\frac{b^{18}}{a^{\frac{1}{12} \cdot 6}}$

Step 7.2

Cancel the common factor of $6$ .

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Step 7.2.1

Factor $6$ out of $12$ .

$\frac{b^{18}}{a^{\frac{1}{6 (2)} \cdot 6}}$

Step 7.2.2

Cancel the common factor.

$\frac{b^{18}}{a^{\frac{1}{6 \cdot 2} \cdot 6}}$

Step 7.2.3

Rewrite the expression.

$\frac{b^{18}}{a^{\frac{1}{2}}}$