Final answer:
The expression (-27x6z4 / y-3)(2/3) simplifies to -9x4z(8/3)y-2, which is option A in the question given.
Step-by-step explanation:
The student's question involves simplifying the expression (-27x6z4 / y-3)(2/3). We start by applying the exponent of (2/3) to each factor within the parentheses.
First, (-27)(2/3) is equal to the cube root of (-27)2, which simplifies to -9.
Next, (x6)(2/3) equals x4 because multiplying the exponents 6 and (2/3) gives us 4.
Similarly, (z4)(2/3) equals z(8/3) because multiplying the exponents 4 and (2/3) gives us (8/3).
Lastly, (y-3)(2/3) is equal to y-2 because multiplying the exponents -3 and (2/3) gives us -2.
Putting it all together, we get the simplified expression -9x4z(8/3)y-2 which corresponds to option A).