All GMAT Math Resources
Example Question #1 : Understanding Exponents
cannot be determined
Putting these together,
Example Question #2 : Understanding Exponents
Example Question #3 : Understanding Exponents
Then putting them together,
Example Question #4 : Understanding Exponents
Which of the following expressions is equivalent to this expression?
You may assume that .
Example Question #5 : Understanding Exponents
Simplify the following expression without a calculator:
The easiest way to simplify is to work from the inside out. We should first get rid of the negatives in the exponents. Remember that variables with negative exponents are equal to the inverse of the expression with the opposite sign. For example, So using this, we simplify:
Now when we multiply variables with exponents, to combine them, we add the exponents together. For example,
Doing this to our expression we get it simplified to .
The next step is taking the inside expression and exponentiating it. When taking an exponent of a variable with an exponent, we actually multiply the exponents. For example, . The other rule we must know that is an exponent of one half is the same as taking the square root. So for the So using these rules,
Example Question #6 : Understanding Exponents
Rewrite as a single logarithmic expression:
First, write each expression as a base 3 logarithm:
Rewrite the expression accordingly, and apply the logarithm sum and difference rules:
Example Question #7 : Understanding Exponents
If , what is in terms of ?
We have .
So , and .
Example Question #8 : Understanding Exponents
What are the last two digits, in order, of ?
Inspect the first few powers of 6; a pattern emerges.
As you can see, the last two digits repeat in a cycle of 5.
789 divided by 5 yields a remainder of 4; the pattern that becomes apparent in the above list is that if the exponent divided by 5 yields a remainder of 4, then the power ends in the diigts 96.
Example Question #9 : Understanding Exponents
Which of the following expressions is equal to the expression
Use the properties of exponents as follows:
Example Question #10 : Understanding Exponents
Apply the power of a power principle twice by multiplying exponents: