The expression (p 2/3 / q1/2)- 2/3 can be simplified to p1/6.
The question asks about simplifying the expression (p2/3 / q1/2) - 2/3. To approach this, we'll use the properties of exponents and radicals. According to exponent rules, a negative exponent represents the reciprocal of the base raised to the positive exponent. Therefore, x-n is equivalent to 1/xn.
The expression (p2/3 / q1/2) - 2/3 can be simplified as follows:
Apply the power rule for division: (p2/3) / (q1/2) = (p2/3) * (q-1/2).
Apply the power rule for multiplication: (p2/3) * (q-1/2) = p2/3 + (-1/2) = p4/6 - 3/6 = p1/6.
Finally, raise p to the power of 1/6 and simplify the expression: (p1/6) - 2/3.
Therefore, the expression (p2/3 / q1/2) - 2/3 is equivalent to p1/6.