Basic Math Examples

$(- 3 a^{5}) (5 a^{- 7})$

Step 1

Rewrite using the commutative property of multiplication.

$- 3 \cdot 5 a^{5} a^{- 7}$

Step 2

Multiply $a^{5}$ by $a^{- 7}$ by adding the exponents.

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Step 2.1

Move $a^{- 7}$ .

$- 3 \cdot 5 (a^{- 7} a^{5})$

Step 2.2

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

$- 3 \cdot 5 a^{- 7 + 5}$

Step 2.3

Add $- 7$ and $5$ .

$- 3 \cdot 5 a^{- 2}$

Step 3

Multiply $- 3$ by $5$ .

$- 15 a^{- 2}$

Step 4

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

$- 15 \frac{1}{a^{2}}$

Step 5

Combine $- 15$ and $\frac{1}{a^{2}}$ .

$\frac{- 15}{a^{2}}$

Step 6

Move the negative in front of the fraction.

$- \frac{15}{a^{2}}$