All ISEE Upper Level Math Resources
Example Questions
Example Question #1 :How To Multiply Exponential Variables
Simplify the following:
None of the other answers
To multiply variables with exponents, add the exponents. With multiple variables, simply add the exponents for each different variable.
Simplified:
Example Question #2 :How To Multiply Exponential Variables
Simplify the following:
None of the other answers
To multiply variables with exponents, add the exponents. When there are constants mixed in, multiply the constants separately and put back in the final result:
Example Question #1 :How To Multiply Exponential Variables
Simplify the following:
To multiply variables with exponents, add the exponents. So,
A longer way would be to write out all the multiplies the exponent tells us to do. This is a little clearer on why adding the exponents works but takes longer and isn't necessary once you understand the process.
Example Question #4 :How To Multiply Exponential Variables
Factor completely:
is the greatest common factor of each term, so distribute it out:
We try to factorby finding two integers with product 4 and sum. However, both of our possible factor pairs fail, sinceand.
is the complete factorization.
Example Question #5 :How To Multiply Exponential Variables
Multiply:
This can be achieved by using the pattern of difference of squares:
Applying the binomial square pattern:
Example Question #6 :How To Multiply Exponential Variables
Factor completely:
The greatest common factor of the terms inis, so factor that out:
Since all factors here are linear, this is the complete factorization.
Example Question #7 :How To Multiply Exponential Variables
Exponentiate:
The cube of a sum pattern can be applied here:
Example Question #8 :How To Multiply Exponential Variables
Write in expanded form:
The cube of a sum pattern can be applied here:
Example Question #9 :How To Multiply Exponential Variables
Factor completely:
The expression cannot be factored.
The expression cannot be factored.
A trinomial with leading coefficientcan be factored by looking for two integers to fill in the boxes:
.
The numbers should have product 20 and sum. However, all of the possible factor pairs fail:
The polynomial is prime.
Example Question #10 :How To Multiply Exponential Variables
Factor completely:
can be seen to be a perfect square trinomial by taking the square root of the first and last terms, multiplying their product by 2, then comparing it to the second term:
Therefore,
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