If f(x)=(x8)2

Question

, what is f(−4)
?(1 point)
f(−4)=

Answer 1

To evaluate $f(-4)$ for the function $f(x)=(x^8{)}^2$:

1. Substitute $-4$ in place of $x$: $$f(-4)=((-4{)}^8{)}^2$$

2. Calculate $(-4{)}^8$: $$(-4{)}^8=(4^8)$$ Since raising a negative number to an even power yields a positive number.

3. Now calculate $4^8$: $$4^8=(4^4{)}^2={256}^2$$ First calculate $4^4$: $$4^4=256$$ Now calculate ${256}^2$: $${256}^2=65536$$ Thus, $(-4{)}^8=65536$.

4. Now, square this result: $$f(-4)=(65536{)}^2$$

5. Calculate ${65536}^2$: $${65536}^2=4294967296$$

Therefore, the final value is: $$f(-4)=4294967296$$