Basic Math Examples

$\frac{{(a^{- 5})}^{3}}{a^{- 5}}$

Step 1

Move $a^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Multiply the exponents in ${(a^{- 5})}^{3}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2

Multiply $- 5$ by $3$ .

$a^{- 15} a^{5}$

Step 3

Multiply $a^{- 15}$ by $a^{5}$ by adding the exponents.

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Step 3.1

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

$a^{- 15 + 5}$

Step 3.2

Add $- 15$ and $5$ .

$a^{- 10}$

Step 4

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

$\frac{1}{a^{10}}$