Question

PLEASE HELP ASAP 50 POINTS BRAINLIEST IF CORRECT

Answer 1

I think the answer is B

Answer 2

Answer:

$f(x)=4^{2x}$

Step-by-step explanation:

So we are given:

$f(x)=(8^{\frac{2}{3}x})(16^{\frac{1}{2}x})$

and we have to find a function that will produce a similar graph. To do this, lets first simplify the given function.

Here are some properties of exponents that I will be using:

$c^{\frac{n}{x}}=\sqrt[x]{c^{n}}=(\sqrt[x]{c})^{n}$

$(c^{x})^{n}=(c^{n})^{x}=c^{xn}$

$c^{x}*c^{n}=c^{x+n}$

Now lets begin simplifying the function.

$f(x)=(8^{\frac{2}{3}x})(16^{\frac{1}{2}x})$

$=((\sqrt[3]{8^{2}})^{x})((\sqrt{16})^{x})$

$=(4^{x})(4^{x})$

$=4^{2x}$

So the correct answer would be $f(x)=4^{2x}$.

I hope you find my answer and explanation to be helpful. Happy studying.