Question

Can someone check a question for me?

Answer 1

I believe it is A after doing everything. @priyar

Answer 2

for "cube roots" (another way to say the ⅓ power)
we look for triples inside the radical.

As you know, when we multiply two radicals we can put "everything inside" (as long as they are the *same power* ⅓ in this case)

so you could write it like this:
\[ \sqrt[3]{4x^2\cdot 8 x^7} = \sqrt{ 2\cdot 2 \cdot 2\cdot 2 \cdot 2 \cdot x^3 \cdot x^3 \cdot x^3}\]
we could expand out x^2*x^7 into a string of 9 x's, but it's easier to write it the way I did
now look for 3 of the same thing: we have 3 2's (and two 2's left over)
and we have 3 of x^3
pull out each triple, but write only one of the triple outside
in other words
\[ 2 x^3 \sqrt[3]{2\cdot 2 }\]
and simplify 2*2 back to 4 to get the final result

Answer 3

So, I was correct? @phi

Answer 4

yes

Answer 5

Thank you! And thank you for providing that explanation as well! (: