Pre-Algebra Examples

$(3 a) (a^{- 3})$

Step 1

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

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Step 1.1

Move $a^{- 3}$ .

$3 (a^{- 3} a)$

Step 1.2

Multiply $a^{- 3}$ by $a$ .

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Step 1.2.1

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

$3 (a^{- 3} a^{1})$

Step 1.2.2

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

$3 a^{- 3 + 1}$

Step 1.3

Add $- 3$ and $1$ .

$3 a^{- 2}$

Step 2

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

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

Step 3

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

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