What is the value of 10 to the -2 power?

To determine the value of 10 raised to the power of -2, it's important to understand the concept of negative exponents. A negative exponent indicates that the base should be taken as the reciprocal and then raised to the positive corresponding exponent.

In this case, 10 to the -2 power can be expressed as the reciprocal of 10 squared. This means:

[ 10^{-2} = \frac{1}{10^2} ]

Calculating (10^2):

[ 10^2 = 10 \times 10 = 100 ]

Now, taking the reciprocal of 100 gives:

[ \frac{1}{100} = 0.01 ]

Thus, the value of 10 to the -2 power equals 0.01, which supports the conclusion that the correct answer is indeed 0.01. Understanding negative exponents in this way is crucial in mathematics, especially in dealing with expressions involving powers and roots.