Calculus Examples

$f (- 64) = 16 - x^{\frac{2}{3}}$

Step 1

Replace the variable $x$ with $- 64$ in the expression.

$f (- 64) = 16 - {(- 64)}^{\frac{2}{3}}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite $- 64$ as ${(- 4)}^{3}$ .

$f (- 64) = 16 - {({(- 4)}^{3})}^{\frac{2}{3}}$

Step 2.1.2

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

$f (- 64) = 16 - {(- 4)}^{3 (\frac{2}{3})}$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Cancel the common factor.

$f (- 64) = 16 - {(- 4)}^{3 (\frac{2}{3})}$

Step 2.1.3.2

Rewrite the expression.

$f (- 64) = 16 - {(- 4)}^{2}$

Step 2.1.4

Raise $- 4$ to the power of $2$ .

$f (- 64) = 16 - 1 \cdot 16$

Step 2.1.5

Multiply $- 1$ by $16$ .

$f (- 64) = 16 - 16$

Step 2.2

Subtract $16$ from $16$ .

$f (- 64) = 0$

Step 2.3

The final answer is $0$ .

$0$

Step 3