Question

Which expressions are equivalent to 3√128x? Check all that apply. 128 x/3, 128 3/x, (4 3√2)x, (4(2 1/3))x, (2 3√4)x

Answer 1

your answers are A C D

Answer 2

Answer:

Option (3) and (4) are correct.

The equivalent expressions to given expression $\sqrt[3]{128}x$ are $4\sqrt[3]{2}x$ and $4(2)^{\frac{1}{3}}x$

Step-by-step explanation:

Given expression $\sqrt[3]{128}x$

We have to write the simplified  form of the given expressions and choose from the given options.

Consider the given expression $\sqrt[3]{128}x$

factorization is a way of writing a numbers as the product of its prime factors.

Thus,  128 can be written as  2 × 2 × 2 × 2 × 2 × 2 × 2 = $2^7$

So, the given expression $\sqrt[3]{128}x$ is written as $\sqrt[3]{2^7}x$

$\sqrt[3]{2^7}x$  can be written as $4\sqrt[3]{2}x$

Also, $\sqrt[3]{a}=a^{\frac{1}{3} }$

Thus, $4\sqrt[3]{2}x$ is same as writing  $4(2)^{\frac{1}{3}}x$

So, only option (3) and (4) are correct.