Question

Simlify. square root of 5 over cube root of 5

Answer 1

Change these into fractional exponents:

the square root of 3
---------------------------- =
the cube root of 2

3^(½)
---------
2^(⅓)

Now get a common denominator on both fractional exponents:

3^(3/6)
---------
2^(2/6)

To simplify the radical on the bottom we have two 2s so far, but we need 4 more so we can take the 6th root on the bottom. So we will multiply the top and bottom both by
2^(4/6)

3^(3/6)*2^(4/6)
---------------------- =
2^(2/6)*2^(4/6)

Exponents on the bottom together:

3^(3/6)*2^(4/6)
---------------------- =
2^(6/6)

3^(3/6)*2^(4/6)
---------------------- =
.......2

The top can go back into a radical as the sixth root of these factors:

sixth root of [3^(3)*2^(4)]
---------------------------------- =
.......2

Since 3^(3)*2^(4) = 27 * 16 = 432, this becomes:

sixth root of 432
-----------------------
............2

That is as simplified as it gets!!

I hope that helps!! :-)

Answer 2

Here are the options
5 to the power of negative 1 over 6
5 to the power of negative 1 over 6
5 to the power of 5 over 6