Basic Math Examples

$4 w^{- 1} w \cdot 0.5 v^{- 3} y^{- 5} y^{- 6} \cdot 0.4 v^{- 3}$

Step 1

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

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Step 1.1

Move $w$ .

$4 (w \cdot w^{- 1}) \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$

Step 1.2

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

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Step 1.2.1

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

$4 (w^{1} w^{- 1}) \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$

Step 1.2.2

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

$4 w^{1 - 1} \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$

Step 1.3

Subtract $1$ from $1$ .

$4 w^{0} \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$

Step 2

Simplify $4 w^{0} \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$ .

$4 \cdot (0.5 v^{- 3} y^{- 5} y^{- 6}) \cdot (0.4 v^{- 3})$

Step 3

Multiply $v^{- 3}$ by $v^{- 3}$ by adding the exponents.

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Step 3.1

Move $v^{- 3}$ .

$4 \cdot (0.5 (v^{- 3} v^{- 3}) y^{- 5} y^{- 6}) \cdot 0.4$

Step 3.2

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

$4 \cdot (0.5 v^{- 3 - 3} y^{- 5} y^{- 6}) \cdot 0.4$

Step 3.3

Subtract $3$ from $- 3$ .

$4 \cdot (0.5 v^{- 6} y^{- 5} y^{- 6}) \cdot 0.4$

Step 4

Multiply $y^{- 5}$ by $y^{- 6}$ by adding the exponents.

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Step 4.1

Move $y^{- 6}$ .

$4 \cdot (0.5 v^{- 6} (y^{- 6} y^{- 5})) \cdot 0.4$

Step 4.2

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

$4 \cdot (0.5 v^{- 6} y^{- 6 - 5}) \cdot 0.4$

Step 4.3

Subtract $5$ from $- 6$ .

$4 \cdot (0.5 v^{- 6} y^{- 11}) \cdot 0.4$

Step 5

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

$4 \cdot (0.5 \frac{1}{v^{6}} y^{- 11}) \cdot 0.4$

Step 6

Combine $0.5$ and $\frac{1}{v^{6}}$ .

$4 \cdot (\frac{0.5}{v^{6}} y^{- 11}) \cdot 0.4$

Step 7

Cancel the common factor of $0.5$ .

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Step 7.1

Cancel the common factor.

$4 \cdot (\frac{0.5}{v^{6}} y^{- 11}) \cdot 0.4$

Step 7.2

Rewrite the expression.

$4 \cdot (\frac{1}{v^{6}} \cdot \frac{y^{- 11}}{2}) \cdot 0.4$

Step 8

Multiply $\frac{1}{v^{6}}$ by $\frac{y^{- 11}}{2}$ .

$4 \cdot \frac{y^{- 11}}{v^{6} \cdot 2} \cdot 0.4$

Step 9

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

$4 \cdot \frac{\frac{1}{y^{11}}}{v^{6} \cdot 2} \cdot 0.4$

Step 10

Cancel the common factor of $2$ .

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Step 10.1

Factor $2$ out of $4$ .

$2 (2) \cdot \frac{\frac{1}{y^{11}}}{v^{6} \cdot 2} \cdot 0.4$

Step 10.2

Factor $2$ out of $v^{6} \cdot 2$ .

$2 (2) \cdot \frac{\frac{1}{y^{11}}}{2 \cdot v^{6}} \cdot 0.4$

Step 10.3

Cancel the common factor.

$2 \cdot 2 \cdot \frac{\frac{1}{y^{11}}}{2 \cdot v^{6}} \cdot 0.4$

Step 10.4

Rewrite the expression.

$2 \cdot \frac{\frac{1}{y^{11}}}{v^{6}} \cdot 0.4$

Step 11

Combine $2$ and $\frac{\frac{1}{y^{11}}}{v^{6}}$ .

$\frac{2 \frac{1}{y^{11}}}{v^{6}} \cdot 0.4$

Step 12

Combine $2$ and $\frac{1}{y^{11}}$ .

$\frac{\frac{2}{y^{11}}}{v^{6}} \cdot 0.4$

Step 13

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{y^{11}} \cdot \frac{1}{v^{6}} \cdot 0.4$

Step 14

Combine.

$\frac{2 \cdot 1}{y^{11} v^{6}} \cdot 0.4$

Step 15

Multiply $2$ by $1$ .

$\frac{2}{y^{11} v^{6}} \cdot 0.4$

Step 16

Multiply $\frac{2}{y^{11} v^{6}} \cdot 0.4$ .

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Step 16.1

Combine $\frac{2}{y^{11} v^{6}}$ and $0.4$ .

$\frac{2 \cdot 0.4}{y^{11} v^{6}}$

Step 16.2

Multiply $2$ by $0.4$ .

$\frac{0.8}{y^{11} v^{6}}$