Respuesta :
Answer:
Which expression is equal to [tex]\sqrt[3]{64}a^6b^7c^9[/tex]?
The correct answer is B.
[tex]4a^{2}b^{2}c^{3}(\sqrt[3]{b})[/tex]
Step-by-step explanation:
Inside of the radical you have [tex]64a^{6}[/tex]. If you find the cube root of that, you get 4a^2. Go ahead and write that outside of the parenthesis:
[tex]4a^{2}[/tex][tex]\sqrt[x}[/tex][tex]\sqrt[3]({b^{7}c^{9}})[/tex]
If you re-write what is inside of the radical, you get:
[tex]4a^{2}(\sqrt[3]{b^{3}*b^{3}*b^{1}*c^{3}*c^{3}*c^{3} }[/tex]
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:
[tex]4a^{2}b^{2} (\sqrt[3]b*c^{3}*c^{3}*c^{3} })[/tex]
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:
[tex]4a^{2}b^{2}c^{9}(\sqrt[3]b)[/tex]
