Question

(89.06)(1.00625)^12t
Can I multiply these two numbers together even though they have different exponents?

Answer 1

the short answer is no.
But to be more precise, you can multiply the two numbers, and you do it by writing it the way you just did
\[ (89.06)(1.00625)^{12t} \]

what you are asking is, can we *simplify* this number by doing this:
\[ (89.06 \cdot 1.00625)^{12t} \]
and the answer is no. you might know, for example
\[ (a\cdot b)^2 = a^2 \cdot b^2 \]
and using that same idea, we see
\[ (89.06 \cdot 1.00625)^{12t} = 89.06^{12t} \cdot 1.00625^{12t}\]
which is different from
\[ 89.06\cdot 1.00625^{12t}\]

Answer 2

Okay. That explains a lot. Thank you!

Answer 3

if you ever wonder about a simplification, you can test it.
Do it the original way (set t= a number, such as 3),
use your "simplification", set t=3 in that, and see if you get the same result. If you do, your idea (probably) worked. if you get a different answer, you did something not allowed.

Answer 4

Okay; I'll use that tip in the future. Thanks again!