Algebra Examples

$f (x) = - x^{6} + 5 x^{4} + 8 x^{3} + 2 x - 7$ , $x = - 6$

Step 1

Replace the variable $x$ with $- 6$ in the expression.

$f (- 6) = - {(- 6)}^{6} + 5 {(- 6)}^{4} + 8 {(- 6)}^{3} + 2 (- 6) - 7$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $- 6$ to the power of $6$ .

$f (- 6) = - 1 \cdot 46656 + 5 {(- 6)}^{4} + 8 {(- 6)}^{3} + 2 (- 6) - 7$

Step 2.1.2

Multiply $- 1$ by $46656$ .

$f (- 6) = - 46656 + 5 {(- 6)}^{4} + 8 {(- 6)}^{3} + 2 (- 6) - 7$

Step 2.1.3

Raise $- 6$ to the power of $4$ .

$f (- 6) = - 46656 + 5 \cdot 1296 + 8 {(- 6)}^{3} + 2 (- 6) - 7$

Step 2.1.4

Multiply $5$ by $1296$ .

$f (- 6) = - 46656 + 6480 + 8 {(- 6)}^{3} + 2 (- 6) - 7$

Step 2.1.5

Raise $- 6$ to the power of $3$ .

$f (- 6) = - 46656 + 6480 + 8 \cdot - 216 + 2 (- 6) - 7$

Step 2.1.6

Multiply $8$ by $- 216$ .

$f (- 6) = - 46656 + 6480 - 1728 + 2 (- 6) - 7$

Step 2.1.7

Multiply $2$ by $- 6$ .

$f (- 6) = - 46656 + 6480 - 1728 - 12 - 7$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $- 46656$ and $6480$ .

$f (- 6) = - 40176 - 1728 - 12 - 7$

Step 2.2.2

Subtract $1728$ from $- 40176$ .

$f (- 6) = - 41904 - 12 - 7$

Step 2.2.3

Subtract $12$ from $- 41904$ .

$f (- 6) = - 41916 - 7$

Step 2.2.4

Subtract $7$ from $- 41916$ .

$f (- 6) = - 41923$

Step 2.3

The final answer is $- 41923$ .

$- 41923$

Step 3