Finite Math Examples

${(\frac{2}{7})}^{0} - 32^{- \frac{2}{5}}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{2}{7}$ .

$\frac{2^{0}}{7^{0}} - 32^{- \frac{2}{5}}$

Step 1.2

Anything raised to $0$ is $1$ .

$\frac{1}{7^{0}} - 32^{- \frac{2}{5}}$

Step 1.3

Anything raised to $0$ is $1$ .

$\frac{1}{1} - 32^{- \frac{2}{5}}$

Step 1.4

Divide $1$ by $1$ .

$1 - 32^{- \frac{2}{5}}$

Step 1.5

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

$1 - \frac{1}{32^{\frac{2}{5}}}$

Step 1.6

Simplify the denominator.

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Step 1.6.1

Rewrite $32$ as $2^{5}$ .

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

Step 1.6.2

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

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

Step 1.6.3

Cancel the common factor of $5$ .

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Step 1.6.3.1

Cancel the common factor.

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

Step 1.6.3.2

Rewrite the expression.

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

Step 1.6.4

Raise $2$ to the power of $2$ .

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

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $1$ from $4$ .

$\frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$