Pre-Algebra Examples

$(5 y^{- 2}) (3 u^{8}) (4 v^{4} y^{9} v u^{- 8})$

Step 1

Multiply $y^{- 2}$ by $y^{9}$ by adding the exponents.

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Step 1.1

Move $y^{9}$ .

$5 (y^{9} y^{- 2}) (3 u^{8}) (4 v^{4} v u^{- 8})$

Step 1.2

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

$5 y^{9 - 2} (3 u^{8}) (4 v^{4} v u^{- 8})$

Step 1.3

Subtract $2$ from $9$ .

$5 y^{7} (3 u^{8}) (4 v^{4} v u^{- 8})$

Step 2

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

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Step 2.1

Move $u^{- 8}$ .

$5 y^{7} (3 (u^{- 8} u^{8})) (4 v^{4} v)$

Step 2.2

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

$5 y^{7} (3 u^{- 8 + 8}) (4 v^{4} v)$

Step 2.3

Add $- 8$ and $8$ .

$5 y^{7} (3 u^{0}) (4 v^{4} v)$

Step 3

Simplify $5 y^{7} (3 u^{0}) (4 v^{4} v)$ .

$5 y^{7} \cdot 3 (4 v^{4} v)$

Step 4

Multiply $v^{4}$ by $v$ by adding the exponents.

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Step 4.1

Move $v$ .

$5 y^{7} \cdot 3 (4 (v \cdot v^{4}))$

Step 4.2

Multiply $v$ by $v^{4}$ .

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Step 4.2.1

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

$5 y^{7} \cdot 3 (4 (v^{1} v^{4}))$

Step 4.2.2

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

$5 y^{7} \cdot 3 (4 v^{1 + 4})$

Step 4.3

Add $1$ and $4$ .

$5 y^{7} \cdot 3 (4 v^{5})$

Step 5

Multiply $3$ by $5$ .

$15 y^{7} (4 v^{5})$

Step 6

Rewrite using the commutative property of multiplication.

$15 \cdot 4 y^{7} v^{5}$

Step 7

Multiply $15$ by $4$ .

$60 y^{7} v^{5}$