Precalculus Examples

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

Step 1

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

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Step 1.1

Move $b^{3}$ .

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

Step 1.2

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

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

Step 1.3

Add $3$ and $4$ .

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

Step 2

Multiply $b^{7}$ by $b^{- 5}$ by adding the exponents.

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Step 2.1

Move $b^{- 5}$ .

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

Step 2.2

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

$b^{- 5 + 7} (3 a) (2 a^{2})$

Step 2.3

Add $- 5$ and $7$ .

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

Step 3

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

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Step 3.1

Move $a^{2}$ .

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

Step 3.2

Multiply $a^{2}$ by $a$ .

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Step 3.2.1

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

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

Step 3.2.2

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

$b^{2} (3 a^{2 + 1}) \cdot 2$

Step 3.3

Add $2$ and $1$ .

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Multiply $2$ by $3$ .

$6 b^{2} a^{3}$