Basic Math Examples

$\frac{{(3 a^{5})}^{- 2}}{a^{4}}$

Step 1

Move ${(3 a^{5})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{4} {(3 a^{5})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $3 a^{5}$ .

$\frac{1}{a^{4} \cdot 3^{2} {(a^{5})}^{2}}$

Step 2.2

Raise $3$ to the power of $2$ .

$\frac{1}{a^{4} \cdot 9 {(a^{5})}^{2}}$

Step 2.3

Multiply the exponents in ${(a^{5})}^{2}$ .

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Step 2.3.1

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

$\frac{1}{a^{4} \cdot 9 a^{5 \cdot 2}}$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{1}{a^{4} \cdot 9 a^{10}}$

Step 2.4

Multiply $a^{4}$ by $a^{10}$ by adding the exponents.

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Step 2.4.1

Move $a^{10}$ .

$\frac{1}{a^{10} a^{4} \cdot 9}$

Step 2.4.2

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

$\frac{1}{a^{10 + 4} \cdot 9}$

Step 2.4.3

Add $10$ and $4$ .

$\frac{1}{a^{14} \cdot 9}$

Step 3

Move $9$ to the left of $a^{14}$ .

$\frac{1}{9 a^{14}}$