Question

Which expression is equivalent to RootIndex 3 StartRoot 64 a Superscript 6 Baseline b Superscript 7 Baseline c Superscript 9 Baseline EndRoot?
2 a b c squared (RootIndex 3 StartRoot 4 a squared b cubed c EndRoot)
4 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)
8 a cubed b cubed c Superscript 4 Baseline (RootIndex 3 StartRoot b c EndRoot)
8 a squared b squared c cubed (RootIndex 3 StartRoot b EndRoot)

Answer 1

Answer:

Which expression is equal to $\sqrt[3]{64}a^6b^7c^9$?

The correct answer is B.

                 $4a^{2}b^{2}c^{3}(\sqrt[3]{b})$

Step-by-step explanation:

Inside of the radical you have $64a^{6}$. If you find the cube root of that, you get 4a^2. Go ahead and write that outside of the parenthesis:

                     $4a^{2}$$\sqrt[x}$$\sqrt[3]({b^{7}c^{9}})$

If you re-write what is inside of the radical, you get:

                $4a^{2}(\sqrt[3]{b^{3}*b^{3}*b^{1}*c^{3}*c^{3}*c^{3} }$

Basically I expanded what was inside of the radical so I could find the cube roots of b^7 and c^9.

Now, take the cube root of b^7:

                       

                       $4a^{2}b^{2} (\sqrt[3]b*c^{3}*c^{3}*c^{3} })$

Notice how I could only factor out the two "b^3" that were inside the radical symbol, and how I left the b^1 inside the radical symbol because I couldn't factor it out.

Let's now get the cube root of c^9. Since it's a perfect cube, there won't be any "c"s left inside of the radical symbol:

               

                            $4a^{2}b^{2}c^{9}(\sqrt[3]b)$

Answer 2

Answer:

B

Step-by-step explanation: