Basic Math Examples

$3 w^{9} y^{- 4} \cdot (7 w^{- 9} v^{7}) \cdot (2 y v^{- 9})$

Step 1

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

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Step 1.1

Move $w^{- 9}$ .

$3 (w^{- 9} w^{9}) y^{- 4} \cdot (7 v^{7}) \cdot (2 y v^{- 9})$

Step 1.2

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

$3 w^{- 9 + 9} y^{- 4} \cdot (7 v^{7}) \cdot (2 y v^{- 9})$

Step 1.3

Add $- 9$ and $9$ .

$3 w^{0} y^{- 4} \cdot (7 v^{7}) \cdot (2 y v^{- 9})$

Step 2

Simplify $3 w^{0} y^{- 4} \cdot (7 v^{7}) \cdot (2 y v^{- 9})$ .

$3 y^{- 4} \cdot (7 v^{7}) \cdot (2 y v^{- 9})$

Step 3

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

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Step 3.1

Move $y$ .

$3 (y \cdot y^{- 4}) \cdot (7 v^{7}) \cdot (2 v^{- 9})$

Step 3.2

Multiply $y$ by $y^{- 4}$ .

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Step 3.2.1

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

$3 (y^{1} y^{- 4}) \cdot (7 v^{7}) \cdot (2 v^{- 9})$

Step 3.2.2

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

$3 y^{1 - 4} \cdot (7 v^{7}) \cdot (2 v^{- 9})$

Step 3.3

Subtract $4$ from $1$ .

$3 y^{- 3} \cdot (7 v^{7}) \cdot (2 v^{- 9})$

Step 4

Multiply $v^{7}$ by $v^{- 9}$ by adding the exponents.

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Step 4.1

Move $v^{- 9}$ .

$3 y^{- 3} \cdot (7 (v^{- 9} v^{7})) \cdot 2$

Step 4.2

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

$3 y^{- 3} \cdot (7 v^{- 9 + 7}) \cdot 2$

Step 4.3

Add $- 9$ and $7$ .

$3 y^{- 3} \cdot (7 v^{- 2}) \cdot 2$

Step 5

Rewrite using the commutative property of multiplication.

$3 \cdot 7 y^{- 3} v^{- 2} \cdot 2$

Step 6

Multiply $3$ by $7$ .

$21 y^{- 3} v^{- 2} \cdot 2$

Step 7

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

$21 \frac{1}{y^{3}} v^{- 2} \cdot 2$

Step 8

Combine $21$ and $\frac{1}{y^{3}}$ .

$\frac{21}{y^{3}} v^{- 2} \cdot 2$

Step 9

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

$\frac{21}{y^{3}} \cdot \frac{1}{v^{2}} \cdot 2$

Step 10

Combine.

$\frac{21 \cdot 1}{y^{3} v^{2}} \cdot 2$

Step 11

Multiply $21$ by $1$ .

$\frac{21}{y^{3} v^{2}} \cdot 2$

Step 12

Multiply $\frac{21}{y^{3} v^{2}} \cdot 2$ .

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Step 12.1

Combine $\frac{21}{y^{3} v^{2}}$ and $2$ .

$\frac{21 \cdot 2}{y^{3} v^{2}}$

Step 12.2

Multiply $21$ by $2$ .

$\frac{42}{y^{3} v^{2}}$