(-x^3/2÷x^-1/3)^3

To simplify the given expression, we need to apply the rules of exponents.

We have:

(-x^(3/2) ÷ x^(-1/3))^3

To divide two similar bases (in this case, both are 'x'), we can subtract the exponents, so:

(-x^(3/2 - (-1/3)))^3

Simplifying the exponent, we have:

(-x^(3/2 + 1/3))^3

Combining the fractions, we have:

(-x^(9/6 + 2/6))^3

(x^(11/6))^3

Applying the rule of exponentiation (raising a power to another power), we multiply the exponents:

x^(11/6 * 3)

x^(33/6)

Further simplifying, we get:

x^(11/2)

Therefore, the simplified expression is x^(11/2).