Question

Which expressions are equivalent to ? Check all that apply.

Answer 1

well, we know x^(1/2) = √(x^1)

so, by that logic we know when a number n is raised to some fraction(x/y) then the numerator is the number n is raised to under the (denomenator) yth root.

So, the third root of 128^x= 128^(x/3)
Also, if we divide 128 by 4^3(64) we get 2. doing this allows us to put 4 outside the 3rd root and leave 2^x under the third root.

I would say the first, 3rd, and 4th answers should be correct and all equivilant to the third root of 128^x. (raising a number to (1/3) is = to taking the 3rd root of that number. this is why 3&4 are both equal)

Answer 2

The given expression can be evaluated by the help of arithmatic operations and the expression can be written as $(128)^{\frac{x}{3}}$, $(4\sqrt[3]{2} )^x$ and $(4 \times (2)^{\frac{1}{3}})^x$.

Given :

Expression - $\sqrt[3]{128^x}$

Arithmatic operations can be used to evaluate the given expression. The steps to evaluate the expression are as follows:

• Step 1 - Rewrite the given expression.

        $= (128)^{\frac{x}{3}}$

• Step 2 - Rewrite 128 as $2\times 2^6$

        $=(2\times 2^6)^{\frac{x}{3}}$

• Step 3 - Rearrange the given expression.

        $= ((2\times2^6)^{\frac{1}{3}})^x = ((2)^{\frac{1}{3}}\times (2^6)^{\frac{1}{3}})^x$

• Step 4 - Now,  $(2^6)^{\frac{1}{3}}$  becomes $2^2$ .

        $=( 2^2 \times 2^{\frac{1}{3}})^x$

        $= (4\times \sqrt[3]{2} )^x$

Therefore, the correct option is A), C), and D).

For more information, refer the link given below

https://brainly.com/question/22687297