Basic Math Examples

$a^{2} b^{3} a^{- 1} b^{2} a b^{- 4}$

Step 1

Multiply $a^{2}$ by $a^{- 1}$ by adding the exponents.

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Step 1.1

Move $a^{- 1}$ .

$a^{- 1} a^{2} b^{3} b^{2} a b^{- 4}$

Step 1.2

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

$a^{- 1 + 2} b^{3} b^{2} a b^{- 4}$

Step 1.3

Add $- 1$ and $2$ .

$a^{1} b^{3} b^{2} a b^{- 4}$

Step 2

Simplify $a^{1} b^{3} b^{2} a b^{- 4}$ .

$a b^{3} b^{2} a b^{- 4}$

Step 3

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1

Move $a$ .

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

Step 3.2

Multiply $a$ by $a$ .

$a^{2} b^{3} b^{2} b^{- 4}$

Step 4

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

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Step 4.1

Move $b^{2}$ .

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

Step 4.2

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

$a^{2} b^{2 + 3} b^{- 4}$

Step 4.3

Add $2$ and $3$ .

$a^{2} b^{5} b^{- 4}$

Step 5

Multiply $b^{5}$ by $b^{- 4}$ by adding the exponents.

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Step 5.1

Move $b^{- 4}$ .

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

Step 5.2

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

$a^{2} b^{- 4 + 5}$

Step 5.3

Add $- 4$ and $5$ .

$a^{2} b^{1}$

Step 6

Simplify $a^{2} b^{1}$ .

$a^{2} b$