Basic Math Examples

$3 a^{- 2} b^{0} \cdot (3 a^{- 5} b^{- 5}) \cdot (4 a^{2} b^{3})$

Step 1

Multiply $a^{- 2}$ by $a^{- 5}$ by adding the exponents.

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Step 1.1

Move $a^{- 5}$ .

$3 (a^{- 5} a^{- 2}) b^{0} \cdot (3 b^{- 5}) \cdot (4 a^{2} b^{3})$

Step 1.2

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

$3 a^{- 5 - 2} b^{0} \cdot (3 b^{- 5}) \cdot (4 a^{2} b^{3})$

Step 1.3

Subtract $2$ from $- 5$ .

$3 a^{- 7} b^{0} \cdot (3 b^{- 5}) \cdot (4 a^{2} b^{3})$

Step 2

Simplify $3 a^{- 7} b^{0} \cdot (3 b^{- 5}) \cdot (4 a^{2} b^{3})$ .

$3 a^{- 7} \cdot (3 b^{- 5}) \cdot (4 a^{2} b^{3})$

Step 3

Multiply $a^{- 7}$ by $a^{2}$ by adding the exponents.

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Step 3.1

Move $a^{2}$ .

$3 (a^{2} a^{- 7}) \cdot (3 b^{- 5}) \cdot (4 b^{3})$

Step 3.2

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

$3 a^{2 - 7} \cdot (3 b^{- 5}) \cdot (4 b^{3})$

Step 3.3

Subtract $7$ from $2$ .

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

Step 4

Multiply $b^{- 5}$ by $b^{3}$ by adding the exponents.

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Step 4.1

Move $b^{3}$ .

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

Step 4.2

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

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

Step 4.3

Subtract $5$ from $3$ .

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

Multiply $3$ by $3$ .

$9 a^{- 5} b^{- 2} \cdot 4$

Step 7

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

$9 \frac{1}{a^{5}} b^{- 2} \cdot 4$

Step 8

Combine $9$ and $\frac{1}{a^{5}}$ .

$\frac{9}{a^{5}} b^{- 2} \cdot 4$

Step 9

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

$\frac{9}{a^{5}} \cdot \frac{1}{b^{2}} \cdot 4$

Step 10

Combine.

$\frac{9 \cdot 1}{a^{5} b^{2}} \cdot 4$

Step 11

Multiply $9$ by $1$ .

$\frac{9}{a^{5} b^{2}} \cdot 4$

Step 12

Multiply $\frac{9}{a^{5} b^{2}} \cdot 4$ .

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Step 12.1

Combine $\frac{9}{a^{5} b^{2}}$ and $4$ .

$\frac{9 \cdot 4}{a^{5} b^{2}}$

Step 12.2

Multiply $9$ by $4$ .

$\frac{36}{a^{5} b^{2}}$