Basic Math Examples

$\frac{{(a^{5} \cdot a^{9})}^{- 5}}{a^{- 15}}$

Step 1

Move ${(a^{5} \cdot a^{9})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{- 15} {(a^{5} \cdot a^{9})}^{5}}$

Step 2

Multiply $a^{5}$ by $a^{9}$ by adding the exponents.

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Step 2.1

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

$\frac{1}{a^{- 15} {(a^{5 + 9})}^{5}}$

Step 2.2

Add $5$ and $9$ .

$\frac{1}{a^{- 15} {(a^{14})}^{5}}$

Step 3

Simplify the expression.

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Step 3.1

Move $a^{- 15}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{15}}{{(a^{14})}^{5}}$

Step 3.2

Multiply the exponents in ${(a^{14})}^{5}$ .

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Step 3.2.1

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

$\frac{a^{15}}{a^{14 \cdot 5}}$

Step 3.2.2

Multiply $14$ by $5$ .

$\frac{a^{15}}{a^{70}}$

Step 4

Cancel the common factor of $a^{15}$ and $a^{70}$ .

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Step 4.1

Multiply by $1$ .

$\frac{a^{15} \cdot 1}{a^{70}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{15}$ out of $a^{70}$ .

$\frac{a^{15} \cdot 1}{a^{15} a^{55}}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{15} \cdot 1}{a^{15} a^{55}}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{a^{55}}$