Question

In which expression should the exponents be multiplied?

a. (5^3)-4
b. (1/3)^4*(1/3)^7
c. 3^7/3^15
d. 4^5*4^2

Answer 1

If we have the same base, we can do this:
(1/3)^4*(1/3)*7 = (1/3)^(4+7) = (1/3)^11
3^7/3^15 = (3^7)*(3*(-15)) = 3^(7 + (-15)) = 3^(-8) = 1/(3^8)
4^5*4^2 = 4^(5+2) = 4^7