Final answer:
The result of raising (32a^4) to the fifth power is 2^25 * a^20. This is achieved by multiplying the exponents of both the base 32 (which is 2^5) and the variable a, thus getting 2^(5*5) * a^(4*5).
Step-by-step explanation:
The question asks to find the result of (32a^4)^5. When we raise a power to another power, we multiply the exponents according to the mathematical rule. This question involves simplifying an expression with an exponential function. The process requires us to raise both the coefficient 32 and the variable term a^4 to the fifth power.
The fifth power of 32 is 32^5, which simplifies to 2^5 * 2^5 or 2^10. Since 32 is 2 raised to the fifth power (2^5), and when taken to the fifth power again (2^5)^5, it becomes 2^(5*5) or 2^25. For the variable term, we multiply the exponents of a, which becomes a^(4*5) or a^20.
Combining these, we get the final answer of (32a^4)^5 = 2^25 * a^20, which is not one of the answer choices listed. Therefore, there is a mistake in the given choices, and the correct answer is 2^25 * a^20.