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