All GRE Math Resources
Example Questions
Example Question #1 : How To Divide Exponents
Simplify
None
Divide the coefficients and subtract the exponents.
Example Question #2 : How To Divide Exponents
Which of the following is equal to the expression , where
xyz ≠ 0?
z
xyz
z/(xy)
1/y
xy
1/y
(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.
Example Question #1 : How To Divide Exponents
If , then
Cannot be determined
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
Example Question #3 : How To Divide Exponents
If , which of the following is equal to ?
a4
The answer cannot be determined from the above information
a6
a18
a
a18
The numerator is simplified to (by adding the exponents), then cube the result. a24/a6 can then be simplified to .
Example Question #1 : Exponential Operations
[641/2 + (–8)1/3] * [43/16 – 3171/3169] =
30
9
–30
–5
16
–30
Let's look at the two parts of the multiplication separately. Remember that (–8)1/3 will be negative. Then 641/2 + (–8)1/3 = 8 – 2 = 6.
For the second part, we can cancel some exponents to make this much easier. 43/16 = 43/42 = 4. Similarly, 3171/3169 = 3171–169 = 32 = 9. So 43/16 – 3171/3169 = 4 – 9 = –5.
Together, [641/2 + (–8)1/3] * [43/16 – 3171/3169] = 6 * (–5) = –30.
Example Question #2 : Exponential Operations
Evaluate:
Distribute the outside exponents first:
Divide the coefficient by subtracting the denominator exponents from the corresponding numerator exponents:
Example Question #2 : Exponential Operations
The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is .
Now, we can cancel out the from the numerator and denominator and continue simplifying the expression.
Example Question #741 : Algebra
Simplify: y3x4(yx3 + y2x2 + y15 + x22)
y3x12 + y6x8 + y45x4 + y3x88
y4x7 + y5x6 + y18x4 + y3x26
y3x12 + y12x8 + y24x4 + y3x23
2x4y4 + 7y15 + 7x22
y3x12 + y6x8 + y45 + x88
y4x7 + y5x6 + y18x4 + y3x26
When you multiply exponents, you add the common bases:
y4 x7 + y5x6 + y18x4 + y3x26
Example Question #3 : Exponential Operations
Indicate whether Quantity A or Quantity B is greater, or if they are equal, or if there is not enough information given to determine the relationship.
Quantity A:
Quantity B:
Quantity B is greater.
The quantities are equal.
The relationship cannot be determined from the information given.
Quantity A is greater.
Quantity B is greater.
By using exponent rules, we can simplify Quantity B.
Also, we can simplify Quantity A.
Since n is positive,
Example Question #2 : Exponential Operations
If , what is the value of ?
Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).
The term on the right can be rewritten, as 27 is equal to 3 to the third power.
Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.
We now know that the exponents must be equal, and can solve for .