ISEE Upper Level Math : Variables and Exponents

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #123 : Variables

Multiply the following:

Possible Answers:

Correct answer:

Explanation:

To multiply variables with exponents, we will use the following formula:

 

Now, let’s combine the following:

Example Question #311 : Algebraic Concepts

Solve the following:

Possible Answers:

Correct answer:

Explanation:

To multiply like variable with exponents, we will use the following formula:

Also, we will multiply coefficients like normal.  

 

So, we get

 

 

 

Example Question #124 : Variables

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Simplify the following expression:

To combine these, we need to multiply our coefficients and our variables. 

First, multiply the coefficients 

Next, multiply our variables by adding the exponent:

So, we put it all together to get:

Example Question #1 : How To Divide Exponential Variables

Simplify the following:

 

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #1 : How To Divide Exponential Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

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 

Example Question #311 : Algebraic Concepts

If , simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Divide Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Divide Exponential Variables

Simplify if .

Possible Answers:

Correct answer:

Explanation:

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

Next, expand the denominator.

Simplify by canceling terms.

Example Question #1 : How To Divide Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #1 : How To Divide Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

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.

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