Question

Which of the following represents 4 x to the 5 sixths power in radical form?

sixth root of 4 x to the fifth power

4 sixth root of x to the fifth power

fifth power of 4 x to the sixth power

4 fifth power of x to the sixth power

Answer 1

That looks like this\[(4x)^{\frac{ 5 }{ 6 }}\]The denominator in your exponent is always the index. The index is the little number that gets stuck in the "dip" of the radical sign. So this is a 6th root which is indicated as such:\[\sqrt[6]{?}\]

Answer 2

Now whats left is the (4x) and the 5 from the numerator of the exponent. That numerator indicates the power to which the (4x) is raised, as such:

Answer 3

\[\sqrt[6]{(4x)^{5}}\]

Answer 4

It's your first choice in your answers. If you need more practice or help with these, just let us know!