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

B

Explanation:

Answer 2

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})`

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)`