Extracting Factors From Radicals.
To withdraw factors from inside radicals, we need to divide the exponent by the index. The resulting quotient will be the exponent of that factor once outside the radical. The remainder (if any) will be the exponent of the factor left inside the radical.
10.51 Withdraw any factors you can from inside the radical:
5.- We calculate the square root of the numerator and we divide it by the square root of the denominator.
6.- We calculate the radicals of the numerator and denominator separately, as we did in the previous exercise.
7.- We simplify the numerical part inside the cube root (we divide the numerator and denominator by 3 and subtract the exponents of powers with the same base). Then, as we have done before, we withdraw the factors outside the radical:
8.- In this exercise, there are two factors in the numerator and one in the denominator outside the radical. We have to bear in mind that any factors withdrawn from the radical will be multiplied by those found outside. Since they are powers, we will add the exponents with the same bases: