which of the following are equivalent to the expression x^1/3 *x^1/2 select all that apply
A. x^1/2 *1/3
B. x^1/2+1/3
C. x^1/6
D. x^5/6
E. 6 square root x
F. 6 square root x^5
The correct answers are:
C. x^1/6
D. x^5/6
why
When multiplying expressions with the same base, the exponents are added. In this case, with x^1/3 * x^1/2, the exponents are 1/3 and 1/2.
Adding the exponents: 1/3 + 1/2 = 2/6 + 3/6 = 5/6
Therefore, x^1/3 * x^1/2 is equivalent to x^5/6, which is option D.
Option C, x^1/6, is also equivalent to x^5/6 but in a simplified form, as x^(1/6) is the same as x^(5/6).