Finite Math Examples

${(25^{\frac{1}{2}})}^{- 3}$

Step 1

Multiply the exponents in ${(25^{\frac{1}{2}})}^{- 3}$ .

Tap for more steps...

Step 1.1

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

$25^{\frac{1}{2} \cdot - 3}$

Step 1.2

Combine $\frac{1}{2}$ and $- 3$ .

$25^{\frac{- 3}{2}}$

Step 1.3

Move the negative in front of the fraction.

$25^{- \frac{3}{2}}$

Step 2

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

$\frac{1}{25^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $25$ as $5^{2}$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$\frac{1}{5^{3}}$

Step 3.4

Raise $5$ to the power of $3$ .

$\frac{1}{125}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{125}$

Decimal Form:

$0.008$