Basic Math Examples

$7 u - 9 w \cdot (3 y^{- 5}) \cdot (3 u^{9} y^{- 3} w^{- 7})$

Step 1

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

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Step 1.1

Move $w^{- 7}$ .

$7 u - 9 (w^{- 7} w) \cdot (3 y^{- 5}) \cdot (3 u^{9} y^{- 3})$

Step 1.2

Multiply $w^{- 7}$ by $w$ .

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Step 1.2.1

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

$7 u - 9 (w^{- 7} w^{1}) \cdot (3 y^{- 5}) \cdot (3 u^{9} y^{- 3})$

Step 1.2.2

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

$7 u - 9 w^{- 7 + 1} \cdot (3 y^{- 5}) \cdot (3 u^{9} y^{- 3})$

Step 1.3

Add $- 7$ and $1$ .

$7 u - 9 w^{- 6} \cdot (3 y^{- 5}) \cdot (3 u^{9} y^{- 3})$

Step 2

Multiply $y^{- 5}$ by $y^{- 3}$ by adding the exponents.

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Step 2.1

Move $y^{- 3}$ .

$7 u - 9 w^{- 6} \cdot (3 (y^{- 3} y^{- 5})) \cdot (3 u^{9})$

Step 2.2

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

$7 u - 9 w^{- 6} \cdot (3 y^{- 3 - 5}) \cdot (3 u^{9})$

Step 2.3

Subtract $5$ from $- 3$ .

$7 u - 9 w^{- 6} \cdot (3 y^{- 8}) \cdot (3 u^{9})$

Step 3

Rewrite using the commutative property of multiplication.

$7 u - 9 \cdot 3 w^{- 6} y^{- 8} \cdot (3 u^{9})$

Step 4

Multiply $- 9$ by $3$ .

$7 u - 27 w^{- 6} y^{- 8} \cdot (3 u^{9})$

Step 5

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

$7 u - 27 \frac{1}{w^{6}} y^{- 8} \cdot (3 u^{9})$

Step 6

Combine $- 27$ and $\frac{1}{w^{6}}$ .

$7 u + \frac{- 27}{w^{6}} y^{- 8} \cdot (3 u^{9})$

Step 7

Rewrite using the commutative property of multiplication.

$7 u + 3 \frac{- 27}{w^{6}} y^{- 8} u^{9}$

Step 8

Move the negative in front of the fraction.

$7 u + 3 (- \frac{27}{w^{6}}) y^{- 8} u^{9}$

Step 9

Multiply $3 (- \frac{27}{w^{6}})$ .

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Step 9.1

Multiply $- 1$ by $3$ .

$7 u - 3 \frac{27}{w^{6}} y^{- 8} u^{9}$

Step 9.2

Combine $- 3$ and $\frac{27}{w^{6}}$ .

$7 u + \frac{- 3 \cdot 27}{w^{6}} y^{- 8} u^{9}$

Step 9.3

Multiply $- 3$ by $27$ .

$7 u + \frac{- 81}{w^{6}} y^{- 8} u^{9}$

Step 10

Move the negative in front of the fraction.

$7 u - \frac{81}{w^{6}} y^{- 8} u^{9}$

Step 11

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

$7 u - \frac{81}{w^{6}} \cdot \frac{1}{y^{8}} u^{9}$

Step 12

Multiply $\frac{1}{y^{8}}$ by $\frac{81}{w^{6}}$ .

$7 u - \frac{81}{y^{8} w^{6}} u^{9}$

Step 13

Combine $u^{9}$ and $\frac{81}{y^{8} w^{6}}$ .

$7 u - \frac{u^{9} \cdot 81}{y^{8} w^{6}}$

Step 14

Move $81$ to the left of $u^{9}$ .

$7 u - \frac{81 u^{9}}{y^{8} w^{6}}$