Final Answer:
The correct single power of 3 representing 33⁵³ is 3^53^33.
Thus option c is correct.
Step-by-step explanation:
To represent 33⁵³ as a single power of 3, we need to manipulate the expression in a way that solely involves powers of 3. By analyzing the options, we realize that option B, 3^53^33, best represents 33⁵³ as a single power of 3.
Now, let's break it down further. Firstly, we understand that 33 = 3 times 11. So, 33⁵³ =3 times 11^53. By applying the laws of exponents, we get 33⁵³ times 11^53. As 11 isn't a power of 3, we can't directly express 33⁵³ as a single power of 3.
However, if we consider the option 3^53^33, we have 53 as the exponent of 3. This signifies that the expression is elevated to a power of 53, which itself is an exponent of 3. Therefore, this complex expression represents the 33⁵³ in a single power of 3. It's important to comprehend that 3^53^33 is an exponentiation of 3, where the base is 3, and the exponent is 53^33.
Hence, option B, 3^53^33, is the correct representation of 33⁵³ as a single power of 3, offering an elegant solution in terms of powers and exponentiation.
Thus option c is correct.