Algebra Examples

$u^{- 1} v^{- 2} \cdot 3 u$

Step 1

Rewrite using the commutative property of multiplication.

$3 u^{- 1} v^{- 2} u$

Step 2

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

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Step 2.1

Move $u$ .

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

Step 2.2

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

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Step 2.2.1

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

$3 (u^{1} u^{- 1}) v^{- 2}$

Step 2.2.2

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

$3 u^{1 - 1} v^{- 2}$

Step 2.3

Subtract $1$ from $1$ .

$3 u^{0} v^{- 2}$

Step 3

Simplify $3 u^{0} v^{- 2}$ .

$3 v^{- 2}$

Step 4

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

$3 \frac{1}{v^{2}}$

Step 5

Combine $3$ and $\frac{1}{v^{2}}$ .

$\frac{3}{v^{2}}$