Basic Math Examples

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

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

Step 1

Multiply

w^{9}

$w^{9}$ by

w^{- 9}

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

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Step 1.1

Move

w^{- 9}

$w^{- 9}$ .

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

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 1.3

Add

- 9

$- 9$ and

9

$9$ .

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

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

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

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

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

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

Step 3

Multiply

y^{- 4}

$y^{- 4}$ by

y

$y$ by adding the exponents.

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Step 3.1

Move

y

$y$ .

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

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

Step 3.2

Multiply

y

$y$ by

y^{- 4}

$y^{- 4}$ .

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Step 3.2.1

Raise

y

$y$ to the power of

1

$1$ .

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

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

Step 3.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 3.3

Subtract

4

$4$ from

1

$1$ .

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

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

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

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

Step 4

Multiply

v^{7}

$v^{7}$ by

v^{- 9}

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

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Step 4.1

Move

v^{- 9}

$v^{- 9}$ .

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

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

Step 4.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 4.3

Add

- 9

$- 9$ and

7

$7$ .

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

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

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

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

Step 5

Rewrite using the commutative property of multiplication.

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

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

Step 6

Multiply

3

$3$ by

7

$7$ .

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

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

Step 7

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 8

Combine

21

$21$ and

\frac{1}{y^{3}}

$\frac{1}{y^{3}}$ .

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

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

Step 9

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 10

Combine.

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

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

Step 11

Multiply

21

$21$ by

1

$1$ .

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

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

Step 12

Multiply

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

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

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Step 12.1

Combine

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

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

2

$2$ .

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

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

Step 12.2

Multiply

21

$21$ by

2

$2$ .

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

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

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

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