Basic Math Examples

$c^{\frac{3}{2}} \div c^{- \frac{1}{2}}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

Multiply $c^{\frac{3}{2}}$ by $c^{\frac{1}{2}}$ 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.

$c^{\frac{3}{2} + \frac{1}{2}}$

Step 3.2

Combine the numerators over the common denominator.

$c^{\frac{3 + 1}{2}}$

Step 3.3

Add $3$ and $1$ .

$c^{\frac{4}{2}}$

Step 3.4

Divide $4$ by $2$ .

$c^{2}$