Final answer:
To simplify (32x^6)^(2/5), you multiply the exponents, resulting in 32^(2/5) as 2^2, which is 4, and x^(12/5), which simplifies to x^2. Thus, the simplified expression is 4x^2, corresponding to option B).
Step-by-step explanation:
To simplify the expression (32x6)2/5, we need to apply the rules of exponents. When we raise a power to a power, we multiply the exponents. Thus, we have:
(32x6)2/5 = 322/5 x6*2/5
Now, simplifying each part individually:
- 322/5 is the 5th root of 32 squared, which is the 5th root of 1024. Since 32 is 25, it simplifies to 25*2/5 = 22, which is 4.
- x6*2/5 simplifies to x12/5 or x2.4, which is the same as x2x2/5. However, the exponent 2/5 doesn't simplify further since it is already in simplest form.
So, combining both parts, we have:
4x2
Therefore, the simplified form of the given expression is 4x2, which corresponds to option B).