## anonymous one year ago Evaluate the following expression. 2^-3

1. UsukiDoll

hey! Long time no see ! :D

2. anonymous

Hi!

3. UsukiDoll

so we are given the problem $\LARGE 2^{-3}$ negative exponents aren't allowed, so we have to take the reciprocal. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For example $\LARGE x^{-2} \rightarrow \frac{1}{x^2}$

4. UsukiDoll

so we need to flip $\LARGE 2^{-3}$ and that becomes ..?

5. anonymous

-3 over 2?

6. UsukiDoll

not exactly... remember our example $\LARGE x^{-2} \rightarrow \frac{1}{x^2}$ so let x =2 and replace the -2 with -3

7. UsukiDoll

A negative exponent is equivalent to the inverse of the same number with a positive exponent

8. UsukiDoll

example $\LARGE x^{-4} \rightarrow \frac{1}{x^4}$

9. anonymous

Oh okay I got it!

10. UsukiDoll

so let's try to apply the example to $\LARGE 2^{-3}$

11. UsukiDoll

so instead of $\LARGE 2^{-3}$ we have $\LARGE 2^{-3} \rightarrow \frac{1}{?}$