Algebra Examples

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

Step 1

Reduce the expression $\frac{a^{\frac{1}{2}}}{a^{2}}$ by cancelling the common factors.

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Step 1.1

Factor $a^{2}$ out of $a^{\frac{1}{2}}$ .

$\frac{a^{2} a^{\frac{- 3}{2}}}{a^{2}}$

Step 1.2

Multiply by $1$ .

$\frac{a^{2} a^{\frac{- 3}{2}}}{a^{2} \cdot 1}$

Step 1.3

Cancel the common factor.

$\frac{a^{2} a^{\frac{- 3}{2}}}{a^{2} \cdot 1}$

Step 1.4

Rewrite the expression.

$\frac{a^{\frac{- 3}{2}}}{1}$

Step 2

Divide $a^{\frac{- 3}{2}}$ by $1$ .

$a^{\frac{- 3}{2}}$

Step 3

Move the negative in front of the fraction.

$a^{- \frac{3}{2}}$

Step 4

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

$\frac{1}{a^{\frac{3}{2}}}$

Step 5

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{1}{\sqrt{a^{3}}}$