Final answer:
To simplify the expression (a⁵.b)(⁻²/⁵/.⁻¹/³), divide the exponent in the denominator, rewrite it as (-2/5)*(-3/1), simplify the result to 2/15, and then multiply the base's exponent with the simplified exponent.
Step-by-step explanation:
To simplify the expression, we need to follow the order of operations. First, we need to simplify the exponent in the denominator. The exponent of the denominator is -2/5/(-1/3).
In order to divide negative exponents, we can rewrite it as (-2/5)*(-3/1). Dividing -2/5 by -3/1 gives us (2/5)*(1/3) = 2/15.
Next, we multiply the exponent of the base with the simplified exponent. The base is a⁵.b and the simplified exponent is 2/15. Therefore, the final simplified expression is (a⁵.b)^(2/15).