Basic Math Examples

$\frac{6 a^{- 4} (3 b^{8})}{3 a^{3} b^{2}}$

Step 1

Move $a^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{6 (3 b^{8})}{3 a^{3} b^{2} a^{4}}$

Step 2

Multiply $a^{3}$ by $a^{4}$ by adding the exponents.

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Step 2.1

Move $a^{4}$ .

$\frac{6 (3 b^{8})}{3 (a^{4} a^{3}) b^{2}}$

Step 2.2

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

$\frac{6 (3 b^{8})}{3 a^{4 + 3} b^{2}}$

Step 2.3

Add $4$ and $3$ .

$\frac{6 (3 b^{8})}{3 a^{7} b^{2}}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

Factor $3$ out of $6 (3 b^{8})$ .

$\frac{3 (2 (3 b^{8}))}{3 a^{7} b^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 a^{7} b^{2}$ .

$\frac{3 (2 (3 b^{8}))}{3 (a^{7} b^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (2 (3 b^{8}))}{3 (a^{7} b^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 (3 b^{8})}{a^{7} b^{2}}$

Step 4

Cancel the common factor of $b^{8}$ and $b^{2}$ .

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Step 4.1

Factor $b^{2}$ out of $2 (3 b^{8})$ .

$\frac{b^{2} (2 (3 b^{6}))}{a^{7} b^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b^{2}$ out of $a^{7} b^{2}$ .

$\frac{b^{2} (2 (3 b^{6}))}{b^{2} a^{7}}$

Step 4.2.2

Cancel the common factor.

$\frac{b^{2} (2 (3 b^{6}))}{b^{2} a^{7}}$

Step 4.2.3

Rewrite the expression.

$\frac{2 (3 b^{6})}{a^{7}}$

Step 5

Multiply $2$ by $3$ .

$\frac{6 b^{6}}{a^{7}}$