Basic Math Examples

5 y^{- 2} y \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 y^{- 2} y \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

Step 1

Multiply

y^{- 2}

$y^{- 2}$ by

y

$y$ by adding the exponents.

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Step 1.1

Move

y

$y$ .

5 (y \cdot y^{- 2}) \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 (y \cdot y^{- 2}) \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

Step 1.2

Multiply

y

$y$ by

y^{- 2}

$y^{- 2}$ .

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Step 1.2.1

Raise

y

$y$ to the power of

1

$1$ .

5 (y^{1} y^{- 2}) \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 (y^{1} y^{- 2}) \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

Step 1.2.2

Use the power rule

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

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

5 y^{1 - 2} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 y^{1 - 2} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

5 y^{1 - 2} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 y^{1 - 2} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

Step 1.3

Subtract

2

$2$ from

1

$1$ .

5 y^{- 1} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 y^{- 1} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

5 y^{- 1} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)

$5 y^{- 1} \cdot (2 v^{- 1} u^{9} u^{- 7}) \cdot (2 v)$

Step 2

Multiply

v^{- 1}

$v^{- 1}$ by

v

$v$ by adding the exponents.

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Step 2.1

Move

v

$v$ .

5 y^{- 1} \cdot (2 (v \cdot v^{- 1}) u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 (v \cdot v^{- 1}) u^{9} u^{- 7}) \cdot 2$

Step 2.2

Multiply

v

$v$ by

v^{- 1}

$v^{- 1}$ .

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Step 2.2.1

Raise

v

$v$ to the power of

1

$1$ .

5 y^{- 1} \cdot (2 (v^{1} v^{- 1}) u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 (v^{1} v^{- 1}) u^{9} u^{- 7}) \cdot 2$

Step 2.2.2

Use the power rule

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

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

5 y^{- 1} \cdot (2 v^{1 - 1} u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 v^{1 - 1} u^{9} u^{- 7}) \cdot 2$

5 y^{- 1} \cdot (2 v^{1 - 1} u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 v^{1 - 1} u^{9} u^{- 7}) \cdot 2$

Step 2.3

Subtract

1

$1$ from

1

$1$ .

5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2$

5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2$

Step 3

Simplify

5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 v^{0} u^{9} u^{- 7}) \cdot 2$ .

5 y^{- 1} \cdot (2 u^{9} u^{- 7}) \cdot 2

$5 y^{- 1} \cdot (2 u^{9} u^{- 7}) \cdot 2$

Step 4

Multiply

u^{9}

$u^{9}$ by

u^{- 7}

$u^{- 7}$ by adding the exponents.

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Step 4.1

Move

u^{- 7}

$u^{- 7}$ .

5 y^{- 1} \cdot (2 (u^{- 7} u^{9})) \cdot 2

$5 y^{- 1} \cdot (2 (u^{- 7} u^{9})) \cdot 2$

Step 4.2

Use the power rule

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

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

5 y^{- 1} \cdot (2 u^{- 7 + 9}) \cdot 2

$5 y^{- 1} \cdot (2 u^{- 7 + 9}) \cdot 2$

Step 4.3

Add

- 7

$- 7$ and

9

$9$ .

5 y^{- 1} \cdot (2 u^{2}) \cdot 2

$5 y^{- 1} \cdot (2 u^{2}) \cdot 2$

5 y^{- 1} \cdot (2 u^{2}) \cdot 2

$5 y^{- 1} \cdot (2 u^{2}) \cdot 2$

Step 5

Rewrite using the commutative property of multiplication.

5 \cdot 2 y^{- 1} u^{2} \cdot 2

$5 \cdot 2 y^{- 1} u^{2} \cdot 2$

Step 6

Multiply

5

$5$ by

2

$2$ .

10 y^{- 1} u^{2} \cdot 2

$10 y^{- 1} u^{2} \cdot 2$

Step 7

Rewrite the expression using the negative exponent rule

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

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

10 \frac{1}{y} u^{2} \cdot 2

$10 \frac{1}{y} u^{2} \cdot 2$

Step 8

Combine

10

$10$ and

\frac{1}{y}

$\frac{1}{y}$ .

\frac{10}{y} u^{2} \cdot 2

$\frac{10}{y} u^{2} \cdot 2$

Step 9

Combine

\frac{10}{y}

$\frac{10}{y}$ and

u^{2}

$u^{2}$ .

\frac{10 u^{2}}{y} \cdot 2

$\frac{10 u^{2}}{y} \cdot 2$

Step 10

Multiply

\frac{10 u^{2}}{y} \cdot 2

$\frac{10 u^{2}}{y} \cdot 2$ .

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Step 10.1

Combine

\frac{10 u^{2}}{y}

$\frac{10 u^{2}}{y}$ and

2

$2$ .

\frac{10 u^{2} \cdot 2}{y}

$\frac{10 u^{2} \cdot 2}{y}$

Step 10.2

Multiply

2

$2$ by

10

$10$ .

\frac{20 u^{2}}{y}

$\frac{20 u^{2}}{y}$

\frac{20 u^{2}}{y}

$\frac{20 u^{2}}{y}$