Question

Which functions are equivalent to f (x) = RootIndex 4 StartRoot 162 EndRoot Superscript x? Check all that apply.

Answer 1

Answer:

A.B. E.

Step-by-step explanation:

Answer 2

Answer:

$f(x)=162^\frac{x}{4}$

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

$f(x)=[3(2^{\frac{1}{4}})]^{x}$

Step-by-step explanation:

we have

$f(x)=\sqrt[4]{162^{x}}$

Remember that

$\sqrt[n]{a^{m}}=a^{m/n}$

$(a^{m})^{n}=a^{m*n}$

so

1) $\sqrt[4]{162^{x}}=162^\frac{x}{4}$

2) The number 162  decompose in prime factors is

$162=(2)(3^4)$

substitute

$f(x)=\sqrt[4]{[(2)(3^4)]^{x}}={[(2)(3^4)]^{x/4}={{[(2)(3^4)]^{(1/4)}}^x=[3\sqrt[4]{2}]^{x}$

3) $f(x)=[3\sqrt[4]{2}]^{x}=[3(2^{\frac{1}{4}})]^{x}$

therefore

$f(x)=162^\frac{x}{4}$

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

$f(x)=[3(2^{\frac{1}{4}})]^{x}$