Variables and Exponents - ISEE Upper Level Quantitative Reasoning

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify.

This fraction cannot be simplified further.

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify.

The degree of a term of a polynomial with one variable is the exponent of that variable. The terms of a polynomial in standard form are written in descending order of degree. Therefore, we rearrange the terms by their exponent, from 5 down to 0, noting that we can rewrite the and constant terms with exponents 1 and 0, respectively:

Substitute for in the definition:

Start by reordering the expression to group like-terms together.

Combine like-terms to simplify.

We can expand the first term using FOIL:

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

Expand each term by using FOIL:

Rearrange to group like-terms together.

Simplify by combining like-terms.

To divide a variable with an exponent, you can write out all the multiplies, which for this question would look like:

Then cancel out the matching p's, leaving:

Or, if the top and bottom are the same variable, you can simply subtract the bottom exponent from the top exponent.

To divide variables with exponents, either:

Write out the multiplies, then reduce

or subtract the bottom exponent from the top, like so

Remember, negative exponent means dividing. would also be correct, but you should know that is equivalent to

Start by factoring the numerator. can be removed from each term.

Next, expand the denominator.

Simplify by canceling terms.

In the denominator, apply the exponent to the terms in parentheses.

Terms with negative exponents can be inverted within the fraction to eliminate the negative.

Simplify by canceling variables and mulitplying.

Break up the fraction into components with like-terms.

Simplify by combining exponents. Remember that exponents in the denominator will become negative.

Finally, put any negative exponent terms into the denominator.