If 3^a=2 and 7^b=5, then 9^4a * 49^2b =

Question

A. 2^4 * 5^2
B. 2^6 * 5^6
C. 2^8 * 5^4
D. 2^4 * 5^8

How can something to a power be smaller than the number and how do I do this?

Answer 1

if 3^a = 2
then 9^(4a) = (3^2)^(4a)
= (3^a)^8
= 2^8

49^(2b)
= (7^2)^(2b)
= (7^b)^(4)
= 5^8

then 9^4a * 49^2b
= (2^8)(5^4) ------> C