Question

The cube root of 5 times the square root of 5 over the cube root of 5 to the 5th power

Answer 1

(cube root of 5) * sqrt(5)
--------------------------------- = ?
(cube root of 5^5)

This becomes easier if we switch to fractional exponents:


5^(1/3) * 5^(1/2) 5^(1/3 + 1/2) 5^(5/6)
------------------------ = --------------------- = ------------- = 5^[5/6 - 5/3]
[ 5^5 ]^(1/3) 5^(5/3) 5^(5/3)

Note that 5/6 - 5/3 = 5/6 - 10/6 = -5/6.

1
Thus, 5^[5/6 - 5/3] = 5^(-5/6) = --------------
5^(5/6)

That's the correct answer. But if you want to remove the fractional exponent from the denominator, do this:

1 5^(1/6) 5^(1/6)
---------- * ------------- = -------------- (ANSWER)
5^(5/6) 5^(1/6) 5