Finite Math Examples

$- {(\frac{25}{16})}^{\frac{1}{2}}$

Step 1

Apply the product rule to $\frac{25}{16}$ .

$- \frac{25^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 2

Simplify the numerator.

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Step 2.1

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

$- \frac{{(5^{2})}^{\frac{1}{2}}}{16^{\frac{1}{2}}}$

Step 2.2

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

$- \frac{5^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$- \frac{5^{2 (\frac{1}{2})}}{16^{\frac{1}{2}}}$

Step 2.3.2

Rewrite the expression.

$- \frac{5^{1}}{16^{\frac{1}{2}}}$

Step 2.4

Evaluate the exponent.

$- \frac{5}{16^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $16$ as $4^{2}$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$- \frac{5}{4^{1}}$

Step 3.4

Evaluate the exponent.

$- \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{4}$

Decimal Form:

$- 1.25$

Mixed Number Form:

$- 1 \frac{1}{4}$