Evaluate the Function f(x)=x^5-47x^3-16x^2+8x+52 at x=7

$f (x) = x^{5} - 47 x^{3} - 16 x^{2} + 8 x + 52$ at $x = 7$

Replace the variable $x$ with $7$ in the expression.

$f (7) = {(7)}^{5} - 47 {(7)}^{3} - 16 {(7)}^{2} + 8 (7) + 52$

Simplify the result.

Simplify each term.

Raise $7$ to the power of $5$ .

$f (7) = 16807 - 47 {(7)}^{3} - 16 {(7)}^{2} + 8 (7) + 52$

Raise $7$ to the power of $3$ .

$f (7) = 16807 - 47 \cdot 343 - 16 {(7)}^{2} + 8 (7) + 52$

Multiply $- 47$ by $343$ .

$f (7) = 16807 - 16121 - 16 {(7)}^{2} + 8 (7) + 52$

Raise $7$ to the power of $2$ .

$f (7) = 16807 - 16121 - 16 \cdot 49 + 8 (7) + 52$

Multiply $- 16$ by $49$ .

$f (7) = 16807 - 16121 - 784 + 8 (7) + 52$

Multiply $8$ by $7$ .

$f (7) = 16807 - 16121 - 784 + 56 + 52$

Simplify by adding and subtracting.

Subtract $16121$ from $16807$ .

$f (7) = 686 - 784 + 56 + 52$

Subtract $784$ from $686$ .

$f (7) = - 98 + 56 + 52$

Add $- 98$ and $56$ .

$f (7) = - 42 + 52$

Add $- 42$ and $52$ .

$f (7) = 10$

The final answer is $10$ .

$10$