Was the problem given as a quotient of twopowers, like this:? or was it given equivalently as a quotient of two cube roots, like this:? Regardless, consider it as in the above form. Separate the 3 coefficient of the numerator out in front as a coefficient of the entire fraction: A quotient of cube roots can be written as the cube root of a quotient: Under the cube root, we divide the 3 on the bottom into the 81 in the top, getting 27, and we divide the b4 in the bottom into the b10 on top by subtracting exponents getting b6. and we have this: We know the cube root of 27 is 3 so we can take the 27 out of the cube root radical and put a 3 in front of the cube root radical. We can also take the cube root of b6 by dividing the exponent 6 by the index of the radical 3, getting b2 in front of the radical. So we have We can multiple the 3's in front getting 9 and eliminate the parentheses: We haven't finished because we have an exponent 5 under a radical that is larger than the index of the radical, 3, since it is a cube root. So we write the exponent 5 in terms of the largest possible multiple of the radical index, 3. The largest multiple of 3 that does not exceed 5 is 3 itself. Therefore we write the 5 exponent as 3+2: Then we remember the rule for adding exponents when we multiply in reverse and change a3+2 to ała˛: Finally we can take the cube root of ał out on front of the radical as just "a" and our final answer is: Edwin