Question

If a ^20 = (a^n)^m, which of the following could be values for m and n?obA) m = -5, n = -4B) m = 10, n = 10C) m = 22, n = -2D) m = 15, n = 5d

Answer 1

a ^20 = (a^n)^m

When we have a number raised to a power two time, we can multiply the powers;

(a^n)^m = a ^ (n x m)

So, since both sides have the same base:

a^20 = a^ (nxm)

20 = n x m

So, the product of n and m must be 20

A) -5 x -4 = 20

B) 10 x 10 =100

c) 22 x -2 =-44

d)15 x 5 = 75

The correct answer is A.