Simplifying Exponents - Math

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:

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.

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

When dividing with exponents, the exponent in the denominator is subtracted from the exponent in the numerator. For example: .

In our problem, each term can be treated in this manner. Remember that a negative exponent can be moved to the denominator.

Now, simplifly the numerals.

Rewrite each side of the equation to only use a base 2:

The only way this equation can be true is if the exponents are equal.

So:

The on each side cancel, and moving the to the left side, we get:

First simplify the second term, and then combine the two:

We are given: .

Recall that when we are multiplying exponents with the same base, we keep the base the same and add the exponents.

Thus, we have .

Recall that when we are dividing exponents with the same base, we keep the base the same and subtract the exponents.

Thus, we have .

We also recall that for negative exponents,

.

Thus, .

Begin by rearranging the terms in the numerator and denominator so that the exponents are positive:

Multiply the exponents:

Simplify:

First, combine exponents of like variables. This gives us

First, combine exponents of like variables. This gives us which simplifies to

When multiplying exponents with the same base, you just have to add the exponents.

When dividing exponents with the same base, we just subtract the exponents.

When dividing exponents with the same base, we just subtract the exponents.

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

When multiplying exponents with the same base, we add the exponents and keep the base the same.

When multiplying exponents with the same base, we add the exponents and keep the base the same.

When multiplying exponents with the same base, we add the exponents and keep the base the same.

When multiplying exponents with the same base, we just keep the base the same and add the exponents.