Final answer:
To simplify the expression, combine the exponents and simplify the terms. The expression simplifies to z^(1/2)/√z.
Step-by-step explanation:
To simplify the expression, we can use the rules of exponents. First, we need to combine the exponents for each term. For the numerator, z² has an exponent of 2/3, and for the denominator, z⁻³/² has an exponent of -3/2. So, combining the exponents, we have z² * z⁻³/² = z² * (z⁻³)^(1/2) = z² * 1/z^(3/2) = z²/z^(3/2) = z^(2 - 3/2) = z^(1/2).
Next, we need to simplify the expression in the denominator, z¹/². Since z is already raised to the power of 1/2, this term simplifies to √z.
Combining the simplified numerator and denominator, the expression becomes z^(1/2)/√z.