Final answer:
The expression ((m^(2))/(m^((1)/(3))))^(-(1)/(2)) simplifies to m^(-5/6) or 1/(m^(5/6)) by subtracting exponents when dividing with the same base and then multiplying the exponents when taking a power of a power.
Step-by-step explanation:
The expression ((m^(2))/(m^((1)/(3))))^(-(1)/(2)) is equivalent to simplifying both the numerator and denominator to get a single exponent for m. First, we use the property of exponents that states when we divide like bases, we subtract the exponents. So m^(2) divided by m^((1)/(3)) results in m^(2 - (1)/(3)) or m^((6/3)-(1/3)) which simplifies to m^((5/3)).
Next, we take the negative half power of m^((5/3)) which is (m^((5/3)))^(-(1)/(2)). The rule for exponents when raising a power to another power is to multiply the exponents. Therefore, we multiply (5/3) * (-(1)/(2)) = -5/6. The final expression is m^(-5/6), which is equivalent to 1/(m^(5/6)) since a negative exponent indicates a reciprocal.