Question

Which function has a simplified base of 4^sqrt 4 ?

Answer 1

Answer:

c is your answer just took the quiz

Step-by-step explanation:

Answer 2

Answer:

f(x) = $4^{(\sqrt[3]{64} )^{2x}}$.

Step-by-step explanation:

We are given functions

$f(x) = 2^{(\sqrt[3]{16} )}$

f(x) = $2^{(\sqrt[3]{64} )}$

f(x) = $4{(\sqrt[3]{12})^{2x}}$

f(x) = $4^{(\sqrt[3]{64} )^{2x}}$.

We need to find the function with simplified base of 4.

Let us simplify each of the function one by one.

On simplifying exponent in$2^{(\sqrt[3]{16} )}$, we get $2^{(2\sqrt[3]{2} )}$.

On simplifying exponent in $2^{(\sqrt[3]{64} )}$ we get 2^{4}.

On simplifying $4{(\sqrt[3]{12})^{2x}}$ we get $4\left(\sqrt[3]{12}\:\:\right)\left(\sqrt[3]{12}\:\:\right)^x=4\left(\sqrt[3]{12\cdot 12}\right)\:^x=4\left(2\sqrt[3]{18}\right)^x$.

On simplifying $4^{(\sqrt[3]{64} )^{2x}}$ we get $4^{\left(\sqrt[3]{64}\:\right)^{2x}}=4^{\left(4\:\right)^{2x}}=\:4^{16^x}.$

Therefore, fourth function f(x) = $4^{(\sqrt[3]{64} )^{2x}}$ has simplified base 4.