Question

What is the simplified base for the function f(x)=2 (3 sqrt 27^2x)?

Answer 1

C: 9 would be the answer 

Answer 2

Answer:

Option 3 - 9

Step-by-step explanation:

Given : Function $f(x) = 2^{\sqrt[3]{27^{2x}}}$

To find : What is the simplified base for the function ?

Solution :

Step 1 - Write the expression

$f(x) = 2^{\sqrt[3]{27^{2x}}}$

Step 2 - Write 27 as $27=3^3$

$f(x) = 2^{\sqrt[3]{(3^3)^{2x}}}$

Step 3 - Using exponent rules

$(x^m)^n = x^{mn}$

 $f(x) = 2^{\sqrt[3]{3^{6x}}}$

Step 4 - Apply exponent rule,

$\sqrt[n]{x^b} = x^{\frac{b}{n}}$

 $f(x) = 2^{3^{2x}}}$

Step 5 - Solve

 $f(x) = 2^{9^x}$

The base of the x is 9.

Therefor, Option 3 is correct.