Question

F(x) = (1/4)^x. for x = -3

Answer 1

Plug in -3 for x into the equation.

(1/4)^-3

And solve

(1/4)^-3 = 64

Answer 2

When an exponent is a negative number, it means that the term will be converted into a fraction, with 1 being the numerator, and the entire term being the denominator.

Rewrite the term:

$F(-3) = \frac{1}{4}^{-3}$

$\frac{1}{\frac{1}{4}^3}$

Solve the term in the denominator:

$\frac{1}{4}^3 = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64}$

$\frac{1}{\frac{1}{4}^3} = \frac{1}{\frac{1}{64}}$

There is a fraction within a fraction. In this case, a fraction is the denominator of another fraction. We can multiply out the denominator of the fraction and leave out its numerator to become the denominator of the bigger fraction:

$\frac{1}{\frac{1}{64}} \times \frac{64}{64} = \frac{64}{1} = \boxed{64}$

f(-3) will equal 64.