Basic Math Examples

$5 b^{3} \cdot (3 b^{- 2}) \cdot (4 b^{- 5})$

Step 1

Multiply $b^{3}$ by $b^{- 2}$ by adding the exponents.

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Step 1.1

Move $b^{- 2}$ .

$5 (b^{- 2} b^{3}) \cdot 3 \cdot (4 b^{- 5})$

Step 1.2

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

$5 b^{- 2 + 3} \cdot 3 \cdot (4 b^{- 5})$

Step 1.3

Add $- 2$ and $3$ .

$5 b^{1} \cdot 3 \cdot (4 b^{- 5})$

Step 2

Simplify $5 b^{1} \cdot 3 \cdot (4 b^{- 5})$ .

$5 b \cdot 3 \cdot (4 b^{- 5})$

Step 3

Multiply $b$ by $b^{- 5}$ by adding the exponents.

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Step 3.1

Move $b^{- 5}$ .

$5 (b^{- 5} b) \cdot 3 \cdot 4$

Step 3.2

Multiply $b^{- 5}$ by $b$ .

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Step 3.2.1

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

$5 (b^{- 5} b^{1}) \cdot 3 \cdot 4$

Step 3.2.2

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

$5 b^{- 5 + 1} \cdot 3 \cdot 4$

Step 3.3

Add $- 5$ and $1$ .

$5 b^{- 4} \cdot 3 \cdot 4$

Step 4

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

$5 \frac{1}{b^{4}} \cdot 3 \cdot 4$

Step 5

Combine $5$ and $\frac{1}{b^{4}}$ .

$\frac{5}{b^{4}} \cdot 3 \cdot 4$

Step 6

Multiply $\frac{5}{b^{4}} \cdot 3$ .

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Step 6.1

Combine $\frac{5}{b^{4}}$ and $3$ .

$\frac{5 \cdot 3}{b^{4}} \cdot 4$

Step 6.2

Multiply $5$ by $3$ .

$\frac{15}{b^{4}} \cdot 4$

Step 7

Multiply $\frac{15}{b^{4}} \cdot 4$ .

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Step 7.1

Combine $\frac{15}{b^{4}}$ and $4$ .

$\frac{15 \cdot 4}{b^{4}}$

Step 7.2

Multiply $15$ by $4$ .

$\frac{60}{b^{4}}$