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To express 512 in exponential form, we need to find the base and exponent that, when multiplied together, result in 512.

Let's break down the steps to find the correct answer:

Step 1: Determine the factors of 512
First, we need to find the factors of 512, which are the numbers that can be multiplied together to give the product 512. The factors of 512 are:
1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.

Step 2: Observe the pattern
By observing the factors, we can notice a pattern. If we continuously divide 512 by 2, we will eventually reach 1. This pattern suggests that the base of the exponential form is 2.

Step 3: Determine the exponent
To find the exponent, we need to count the number of times we divided 512 by 2 until we reached 1.

512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

We divided 512 by 2 a total of 9 times to reach 1. Therefore, the exponent is 9.

Step 4: Write the exponential form
Now that we have determined the base and exponent, we can write 512 in exponential form as 2^9. This means that 512 can be expressed as 2 to the power of 9.

Therefore, the correct answer is option C) 29.