Which of the following expressions are equivalent to #1.06^(3t)# ?

A. #1.06^(9t) / 1.06^(3t)#

B. #1.06^(5t) / 1.06^(2t)#

C. #1.06^3 * 1.06^t#

D. #(1.06^t)^3#

1 Answer
George C.
Mar 1, 2018

B. and D.

Explanation:

If #a > 0# then:

#a^b * a^c = a^(b+c)#

#(a^b)^c = a^(bc)#

#a^(-1) = 1/a#

and hence also:

#a^b / a^c = a^(b-c)#

So we find:

A. #1.06^(9t) / 1.06^(3t) = 1.06^(9t-3t) = 1.06^(6t)#

B. #1.06^(5t) / 1.06^(2t) = 1.06^(5t-2t) = 1.06^(3t)#

C. #1.06^3 * 1.06^t = 1.06^(3+t)#

D. #(1.06^t)^3 = 1.06^(t * 3) = 1.06^(3t)#

So the equivalent expressions are B. and D.

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