How do you simplify an expression with exponents

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Simplify the following expression.

Correct answer:

Explanation:

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.

Simplify the following expression. 

Correct answer:

Explanation:

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 .

Simplify the following expression. 

Correct answer:

Explanation:

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, .

Simplify the following exponent expression:

Correct answer:

Explanation:

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

Multiply the exponents:

Simplify:

Simplify the expression:

Correct answer:

Explanation:

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

Solve for : 

Possible Answers:

Cannot be determined from the given information.

Correct answer:

Explanation:

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:

Solve for .

Correct answer:

Explanation:

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

What is the largest positive integer, , such that  is a factor of ?

Explanation:

. Thus,  is equal to 16.

Order the following from least to greatest:

Correct answer:

Explanation:

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: .

Simplify the expression:

Correct answer:

Explanation:

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:

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How do you expand and simplify expressions with exponents?