Distributing Exponents

In order to solve this problem, each of the answer choices needs to be simplified.

Instead of simplifying completely, make all terms into a form such that they have 100 as the exponent. Then they can be easily compared.

, , , and .

Thus, ordering from least to greatest: .

. Thus, is equal to 16.

Begin by distributing the exponent through the parentheses. The power rule dictates that an exponent raised to another exponent means that the two exponents are multiplied:

Any negative exponents can be converted to positive exponents in the denominator of a fraction:

The like terms can be simplified by subtracting the power of the denominator from the power of the numerator:

First, set up the equation: . Simplifying this result gives .