Basic Math Examples

$6 w u^{8} \cdot 3 u^{- 6} y^{3} w^{- 4} \cdot 3 y^{- 3}$

Step 1

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

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Step 1.1

Move $w^{- 4}$ .

$6 (w^{- 4} w) u^{8} \cdot (3 u^{- 6} y^{3}) \cdot (3 y^{- 3})$

Step 1.2

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

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Step 1.2.1

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

$6 (w^{- 4} w^{1}) u^{8} \cdot (3 u^{- 6} y^{3}) \cdot (3 y^{- 3})$

Step 1.2.2

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

$6 w^{- 4 + 1} u^{8} \cdot (3 u^{- 6} y^{3}) \cdot (3 y^{- 3})$

Step 1.3

Add $- 4$ and $1$ .

$6 w^{- 3} u^{8} \cdot (3 u^{- 6} y^{3}) \cdot (3 y^{- 3})$

Step 2

Multiply $u^{8}$ by $u^{- 6}$ by adding the exponents.

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Step 2.1

Move $u^{- 6}$ .

$6 w^{- 3} (u^{- 6} u^{8}) \cdot (3 y^{3}) \cdot (3 y^{- 3})$

Step 2.2

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

$6 w^{- 3} u^{- 6 + 8} \cdot (3 y^{3}) \cdot (3 y^{- 3})$

Step 2.3

Add $- 6$ and $8$ .

$6 w^{- 3} u^{2} \cdot (3 y^{3}) \cdot (3 y^{- 3})$

Step 3

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

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Step 3.1

Move $y^{- 3}$ .

$6 w^{- 3} u^{2} \cdot (3 (y^{- 3} y^{3})) \cdot 3$

Step 3.2

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

$6 w^{- 3} u^{2} \cdot (3 y^{- 3 + 3}) \cdot 3$

Step 3.3

Add $- 3$ and $3$ .

$6 w^{- 3} u^{2} \cdot (3 y^{0}) \cdot 3$

Step 4

Simplify $6 w^{- 3} u^{2} \cdot (3 y^{0}) \cdot 3$ .

$6 w^{- 3} u^{2} \cdot 3 \cdot 3$

Step 5

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

$6 \frac{1}{w^{3}} u^{2} \cdot 3 \cdot 3$

Step 6

Combine $6$ and $\frac{1}{w^{3}}$ .

$\frac{6}{w^{3}} u^{2} \cdot 3 \cdot 3$

Step 7

Combine $\frac{6}{w^{3}}$ and $u^{2}$ .

$\frac{6 u^{2}}{w^{3}} \cdot 3 \cdot 3$

Step 8

Multiply $\frac{6 u^{2}}{w^{3}} \cdot 3$ .

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Step 8.1

Combine $\frac{6 u^{2}}{w^{3}}$ and $3$ .

$\frac{6 u^{2} \cdot 3}{w^{3}} \cdot 3$

Step 8.2

Multiply $3$ by $6$ .

$\frac{18 u^{2}}{w^{3}} \cdot 3$

Step 9

Multiply $\frac{18 u^{2}}{w^{3}} \cdot 3$ .

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Step 9.1

Combine $\frac{18 u^{2}}{w^{3}}$ and $3$ .

$\frac{18 u^{2} \cdot 3}{w^{3}}$

Step 9.2

Multiply $3$ by $18$ .

$\frac{54 u^{2}}{w^{3}}$