Question

What is the simplified base for the function f(x) = 2rootindex 3 startroot 27 endroot superscript 2 x?

Answer 1

Applying exponential properties, the simplified base for the function is given as follows:

$f(x) = 2(3)^{2x}$

What is the function?

The function is represented by the following definition:

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

As an exponent, the function is given by:

$f(x) = 2(27)^{\frac{2x}{3}}$

27 can be simplified as follows:

27 = 3 x 3 x 3 = 3³

Hence:

$f(x) = 2(3^3)^{\frac{2x}{3}}$

Then, the 3 at the exponent multiplies 2x and can be simplified with the 3 of the root, hence:

$f(x) = 2(3)^{\frac{3 \times 2x}{3}} = 2(3)^{2x}$

Hence the simplified base for the function is given as follows:

$f(x) = 2(3)^{2x}$

More can be learned about exponential properties at brainly.com/question/25263760

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