Evaluate each exponential expression: 2^(-4) + 4^(-1)

Question

Accepted Answer

Hello everyone in this video I'm going to be evaluating the expression three to the negative two minus two to the negative three. And in this case you can see that there's two components or two exponents, we have three to the negative two and we have two to the negative three. So in order to combine them I'm going to deal with them separately first. So I have three to the negative two. And recall that negative exponents means that the number can be expressed in the denominator. So three to the negative two becomes 3 1/ squared notice how the negative went away because it's in the denominator now And this becomes 1/9. So following that same process I'm gonna do two to the negative three Is equal to 1/2 to the third and that is equal to 1/8. So now I can rewrite the expression as 1/ -1/8. So now I have a more simplified version of the exponents. However, they still don't have the same denominator so I can't combine them. And in order to combine them I need to find the common greatest common factor between them. And in this case it is 72. So I'm going to multiply the 1/9 by 8/8 and the 18 by 9/9. And when I do this multiplication I get 8/ -9/72 and now I can combine them because they have the same denominator of 72. I can see that this becomes negative 1/72. So this becomes my simplified answer for the expression three to the negative two minus two to the negative three. And when I look at my answer options, I see that a aligns with negative 1/72. Hopefully this video helped and thanks for watching.