Finite Math Examples

$f (x) = {(9 (1) - 1)}^{- \frac{1}{3}}$

Step 1

Rewrite the function as an equation.

$y = {(9 (1) - 1)}^{- \frac{1}{3}}$

Step 2

Simplify ${(9 (1) - 1)}^{- \frac{1}{3}}$ .

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Step 2.1

Multiply $9$ by $1$ .

$y = {(9 - 1)}^{- \frac{1}{3}}$

Step 2.2

Subtract $1$ from $9$ .

$y = 8^{- \frac{1}{3}}$

Step 2.3

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

$y = \frac{1}{8^{\frac{1}{3}}}$

Step 2.4

Simplify the denominator.

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Step 2.4.1

Rewrite $8$ as $2^{3}$ .

$y = \frac{1}{{(2^{3})}^{\frac{1}{3}}}$

Step 2.4.2

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

$y = \frac{1}{2^{3 (\frac{1}{3})}}$

Step 2.4.3

Cancel the common factor of $3$ .

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Step 2.4.3.1

Cancel the common factor.

$y = \frac{1}{2^{3 (\frac{1}{3})}}$

Step 2.4.3.2

Rewrite the expression.

$y = \frac{1}{2^{1}}$

Step 2.4.4

Evaluate the exponent.

$y = \frac{1}{2}$