Algebra Examples

$f (x) = 3 \sqrt[3]{x^{4}} - 3 x^{2} - \frac{64}{x}$ at $x = 8$

Step 1

Replace the variable $x$ with $8$ in the expression.

$f (8) = 3 \sqrt[3]{{(8)}^{4}} - 3 {(8)}^{2} - \frac{64}{8}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $8$ to the power of $4$ .

$f (8) = 3 \sqrt[3]{4096} - 3 {(8)}^{2} - \frac{64}{8}$

Step 2.1.2

Rewrite $4096$ as $16^{3}$ .

$f (8) = 3 \sqrt[3]{16^{3}} - 3 {(8)}^{2} - \frac{64}{8}$

Step 2.1.3

Pull terms out from under the radical, assuming real numbers.

$f (8) = 3 \cdot 16 - 3 {(8)}^{2} - \frac{64}{8}$

Step 2.1.4

Multiply $3$ by $16$ .

$f (8) = 48 - 3 {(8)}^{2} - \frac{64}{8}$

Step 2.1.5

Raise $8$ to the power of $2$ .

$f (8) = 48 - 3 \cdot 64 - \frac{64}{8}$

Step 2.1.6

Multiply $- 3$ by $64$ .

$f (8) = 48 - 192 - \frac{64}{8}$

Step 2.1.7

Divide $64$ by $8$ .

$f (8) = 48 - 192 - 1 \cdot 8$

Step 2.1.8

Multiply $- 1$ by $8$ .

$f (8) = 48 - 192 - 8$

Step 2.2

Simplify by subtracting numbers.

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Step 2.2.1

Subtract $192$ from $48$ .

$f (8) = - 144 - 8$

Step 2.2.2

Subtract $8$ from $- 144$ .

$f (8) = - 152$

Step 2.3

The final answer is $- 152$ .

$- 152$

Step 3