Basic Math Examples

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

Step 1

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

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Step 1.1

Move $y$ .

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

Step 1.2

Multiply $y$ by $y^{- 2}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

Subtract $2$ from $1$ .

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

Step 2

Multiply $v^{- 1}$ by $v$ by adding the exponents.

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Step 2.1

Move $v$ .

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

Step 2.2

Multiply $v$ by $v^{- 1}$ .

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Subtract $1$ from $1$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Move $u^{- 7}$ .

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

Step 4.2

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

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

Step 4.3

Add $- 7$ and $9$ .

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

Multiply $5$ by $2$ .

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

Step 7

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

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

Step 8

Combine $10$ and $\frac{1}{y}$ .

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

Step 9

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

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

Step 10

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

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Step 10.1

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

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

Step 10.2

Multiply $2$ by $10$ .

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