Expert: Josh - 5/7/2009

Question
Quick question: I have to "evaluate" for 2 "to the power of" -3.... when i look at the anser sheet it is saying it should equal 1/8, please explain!!

Answer
Hi Shannon

"2 to the power of 3" is equivalent to multiplying 2 by itself three times. This is the same as 2*2*2=8.

A negative power requires us to find the reciprocal of the number. Here, the "number" refers the same expression without the minus sign in the exponent. In other words, 2^(-3) is the same as 1 divided by 2^3. Hence, we get 1/8.

One way to interpret the minus sign is to treat it as an instruction to simply turn the number up-side-down, writing it in the denominator.

e.g., 2^(-3) = 1/(2*2*2)=1/8
3^(-4) = 1/(3*3*3*3)=1/81