Algebra question : 3^-3*3^-1

Question

Is it 81 or 1/81. Every calculator says 1/81 but the way my professor taught it, it made it seem like it was 81

Answer 1

You are multiplying numbers with common base of 3.  So you just add the exponents.

 

3^{(-3 - 1)} = 3^-4

 

 

Then you perform the reciprocal so that you have a positive exponent.

 

1 / 3⁴

 

 

you got if from here.

Answer 2

(3^-3) (3^-1) = 3^-3+(-1) = 3^-4

 

                             = 1/3⁴ = 1/81