Exponential Notation

Question

Evaluate the following:
x^-4 for x=2

I understand the -(2x2x2x2) equals 16 but the answer in the book says 1/16
How do you get 1/16?

Answer 1

recall some laws of exponents. a term which is raised by a negative number is also equal to its reciprocal raised to that number with positive sign. for example,
3^(-2) = (1/3)^2
thus, we can rewrite it as,
(1/x)^4
substituting x = 2,
(1/2)^4
(1/2)*(1/2)*(1/2)*(1/2)
1/16

hope this helps~ :)

Answer 2

Thanks so much :))