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What is the simplified base for the function [tex]\( f(x) = 2 \left(\frac{3}{27}\right)^{2x} \)[/tex]?

A. 2
B. 3
C. 9
D. 18


Sagot :

Sure! Let's simplify the base for the function [tex]\( f(x) = 2 \left( \frac{3}{272} \right)^x \)[/tex].

1. First, look at the fraction inside the parentheses: [tex]\(\frac{3}{272}\)[/tex].

2. Evaluate the fraction: [tex]\(\frac{3}{272}\)[/tex]. When you divide 3 by 272, you get approximately [tex]\(0.011029411764705883\)[/tex].

So, the simplified base of the function [tex]\( f(x) = 2 \left( \frac{3}{272} \right)^x \)[/tex] is approximately [tex]\( 0.011029411764705883 \)[/tex].

Among the given choices:

- 2
- 3
- 9
- 18

None of these choices match our simplified base value ([tex]\( \approx 0.011029411764705883 \)[/tex]).

Therefore, we can deduce that none of the given options are the correct simplified base. If you seek a more simplified or approximated answer, it might be nearest to 1% or [tex]\( \sim 0.01 \)[/tex].