Basic Math Examples

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

Step 1

Multiply the exponents in ${(a^{5})}^{\frac{1}{2}}$ .

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Step 1.1

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

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

Step 1.2

Combine $5$ and $\frac{1}{2}$ .

$\frac{a^{\frac{5}{2}}}{a^{\frac{9}{2}}}$

Step 2

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

$\frac{1}{a^{\frac{9}{2}} a^{- \frac{5}{2}}}$

Step 3

Multiply $a^{\frac{9}{2}}$ by $a^{- \frac{5}{2}}$ 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.

$\frac{1}{a^{\frac{9}{2} - \frac{5}{2}}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1}{a^{\frac{9 - 5}{2}}}$

Step 3.3

Subtract $5$ from $9$ .

$\frac{1}{a^{\frac{4}{2}}}$

Step 3.4

Divide $4$ by $2$ .

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