Basic Math Examples

$3 u^{- 9} \cdot (5 v^{- 2} u^{8} y^{- 6}) \cdot (2^{2} y)$

Step 1

Multiply $u^{- 9}$ by $u^{8}$ by adding the exponents.

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Step 1.1

Move $u^{8}$ .

$3 (u^{8} u^{- 9}) \cdot (5 v^{- 2} y^{- 6}) \cdot (2^{2} y)$

Step 1.2

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

$3 u^{8 - 9} \cdot (5 v^{- 2} y^{- 6}) \cdot (2^{2} y)$

Step 1.3

Subtract $9$ from $8$ .

$3 u^{- 1} \cdot (5 v^{- 2} y^{- 6}) \cdot (2^{2} y)$

Step 2

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

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Step 2.1

Move $y$ .

$3 u^{- 1} \cdot (5 v^{- 2} (y \cdot y^{- 6})) \cdot 2^{2}$

Step 2.2

Multiply $y$ by $y^{- 6}$ .

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Step 2.2.1

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

$3 u^{- 1} \cdot (5 v^{- 2} (y^{1} y^{- 6})) \cdot 2^{2}$

Step 2.2.2

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

$3 u^{- 1} \cdot (5 v^{- 2} y^{1 - 6}) \cdot 2^{2}$

Step 2.3

Subtract $6$ from $1$ .

$3 u^{- 1} \cdot (5 v^{- 2} y^{- 5}) \cdot 2^{2}$

Step 3

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

$3 \frac{1}{u} \cdot (5 v^{- 2} y^{- 5}) \cdot 2^{2}$

Step 4

Combine $3$ and $\frac{1}{u}$ .

$\frac{3}{u} \cdot (5 v^{- 2} y^{- 5}) \cdot 2^{2}$

Step 5

Rewrite using the commutative property of multiplication.

$5 \frac{3}{u} v^{- 2} y^{- 5} \cdot 2^{2}$

Step 6

Multiply $5 \frac{3}{u}$ .

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Step 6.1

Combine $5$ and $\frac{3}{u}$ .

$\frac{5 \cdot 3}{u} v^{- 2} y^{- 5} \cdot 2^{2}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{15}{u} v^{- 2} y^{- 5} \cdot 2^{2}$

Step 7

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

$\frac{15}{u} \cdot \frac{1}{v^{2}} y^{- 5} \cdot 2^{2}$

Step 8

Combine.

$\frac{15 \cdot 1}{u v^{2}} y^{- 5} \cdot 2^{2}$

Step 9

Multiply $15$ by $1$ .

$\frac{15}{u v^{2}} y^{- 5} \cdot 2^{2}$

Step 10

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

$\frac{15}{u v^{2}} \cdot \frac{1}{y^{5}} \cdot 2^{2}$

Step 11

Combine.

$\frac{15 \cdot 1}{u v^{2} y^{5}} \cdot 2^{2}$

Step 12

Simplify the expression.

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Step 12.1

Multiply $15$ by $1$ .

$\frac{15}{u v^{2} y^{5}} \cdot 2^{2}$

Step 12.2

Raise $2$ to the power of $2$ .

$\frac{15}{u v^{2} y^{5}} \cdot 4$

Step 13

Multiply $\frac{15}{u v^{2} y^{5}} \cdot 4$ .

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Step 13.1

Combine $\frac{15}{u v^{2} y^{5}}$ and $4$ .

$\frac{15 \cdot 4}{u v^{2} y^{5}}$

Step 13.2

Multiply $15$ by $4$ .

$\frac{60}{u v^{2} y^{5}}$