When exponentiating \((2^3)\) to the fifth power, what do you get?

When exponentiating ((2^3)) to the fifth power, you apply the power of a power property of exponents. This property states that when you raise a power to another power, you multiply the exponents.

In this case, you have ((2^3)^5). According to the exponentiation rule, you multiply the exponent (3) by the exponent (5):

[ (2^3)^5 = 2^{3 \times 5} = 2^{15} ]

Therefore, the result of raising ((2^3)) to the fifth power is (2^{15}). This method helps simplify expressions involving exponents and shows how the powers interact with one another when exponentiation is involved. The other options do not accurately reflect this application of exponent rules, as they either miscalculate the multiplication of the exponents or do not raise the base to a power at all.