Precalculus Examples

$b^{4} (\frac{1}{3} b^{2}) (12 b^{- 8})$

Step 1

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

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Step 1.1

Move $b^{2}$ .

$b^{2} b^{4} \frac{1}{3} (12 b^{- 8})$

Step 1.2

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

$b^{2 + 4} \frac{1}{3} (12 b^{- 8})$

Step 1.3

Add $2$ and $4$ .

$b^{6} \frac{1}{3} (12 b^{- 8})$

Step 2

Multiply $b^{6}$ by $b^{- 8}$ by adding the exponents.

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Step 2.1

Move $b^{- 8}$ .

$b^{- 8} b^{6} \frac{1}{3} \cdot 12$

Step 2.2

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

$b^{- 8 + 6} \frac{1}{3} \cdot 12$

Step 2.3

Add $- 8$ and $6$ .

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

Step 3

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

$\frac{1}{b^{2}} \cdot \frac{1}{3} \cdot 12$

Step 4

Combine.

$\frac{1 \cdot 1}{b^{2} \cdot 3} \cdot 12$

Step 5

Multiply $1$ by $1$ .

$\frac{1}{b^{2} \cdot 3} \cdot 12$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Factor $3$ out of $b^{2} \cdot 3$ .

$\frac{1}{3 \cdot b^{2}} \cdot 12$

Step 6.2

Factor $3$ out of $12$ .

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

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

$\frac{1}{b^{2}} \cdot 4$

Step 7

Combine $\frac{1}{b^{2}}$ and $4$ .

$\frac{4}{b^{2}}$