Basic Math Examples

${(2 a^{4} b^{- 6})}^{2} (a^{2} b^{- 2})$

Step 1

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

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

Step 2

Multiply $2 a^{4} \frac{1}{b^{6}}$ .

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Step 2.1

Combine $2$ and $\frac{1}{b^{6}}$ .

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

Step 2.2

Combine $a^{4}$ and $\frac{2}{b^{6}}$ .

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

Step 3

Move $2$ to the left of $a^{4}$ .

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

Step 4

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

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Step 4.1

Apply the product rule to $\frac{2 a^{4}}{b^{6}}$ .

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

Step 4.2

Apply the product rule to $2 a^{4}$ .

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

Step 5

Simplify the numerator.

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Step 5.1

Raise $2$ to the power of $2$ .

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

Step 5.2

Multiply the exponents in ${(a^{4})}^{2}$ .

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Step 5.2.1

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

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

Step 5.2.2

Multiply $4$ by $2$ .

$\frac{4 a^{8}}{{(b^{6})}^{2}} (a^{2} b^{- 2})$

Step 6

Simplify terms.

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Step 6.1

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

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Step 6.1.1

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

$\frac{4 a^{8}}{b^{6 \cdot 2}} (a^{2} b^{- 2})$

Step 6.1.2

Multiply $6$ by $2$ .

$\frac{4 a^{8}}{b^{12}} (a^{2} b^{- 2})$

Step 6.2

Cancel the common factor of $b^{- 2}$ .

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Step 6.2.1

Factor $b^{- 2}$ out of $b^{12}$ .

$\frac{4 a^{8}}{b^{- 2} b^{14}} (a^{2} b^{- 2})$

Step 6.2.2

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

$\frac{4 a^{8}}{b^{- 2} b^{14}} (b^{- 2} a^{2})$

Step 6.2.3

Cancel the common factor.

$\frac{4 a^{8}}{b^{- 2} b^{14}} (b^{- 2} a^{2})$

Step 6.2.4

Rewrite the expression.

$\frac{4 a^{8}}{b^{14}} a^{2}$

Step 6.3

Combine $\frac{4 a^{8}}{b^{14}}$ and $a^{2}$ .

$\frac{4 a^{8} a^{2}}{b^{14}}$

Step 7

Multiply $a^{8}$ by $a^{2}$ by adding the exponents.

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Step 7.1

Move $a^{2}$ .

$\frac{4 (a^{2} a^{8})}{b^{14}}$

Step 7.2

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

$\frac{4 a^{2 + 8}}{b^{14}}$

Step 7.3

Add $2$ and $8$ .

$\frac{4 a^{10}}{b^{14}}$