All SAT Math Resources
Example Questions
Example Question #1 :How To Find Patterns In Exponents
If ax·a4= a12and (by)3= b15, what is the value of x - y?
-9
-2
-4
3
6
3
Multiplying like bases means add the exponents, so x+4 = 12, or x = 8.
Raising a power to a power means multiply the exponents, so 3y = 15, or y = 5.
x - y = 8 - 5 = 3.
Example Question #121 :Exponents
If p and q are positive integrers and 27p= 9q, then what is the value of q in terms of p?
(3/2)p
3p
p
(2/3)p
2p
(3/2)p
The first step is to express both sides of the equation with equal bases, in this case 3. The equation becomes 33p= 32q. So then 3p = 2q, and q = (3/2)p is our answer.
Example Question #251 :Exponents
Simplify 272/3.
729
27
125
9
3
9
272/3is 27 squared and cube-rooted. We want to pick the easier operation first. Here that is the cube root. To see that, try both operations.
272/3= (272)1/3= 7291/3OR
272/3= (271/3)2= 32
Obviously 32is much easier. Either 32or 7291/3will give us the correct answer of 9, but with 32it is readily apparent.
Example Question #122 :Exponents
Ifandare integers and
what is the value of?
To solve this problem, we will have to take the log of both sides to bring down our exponents. By doing this, we will get.
To solve forwe will have to divide both sides of our equation byto get.
will give you the answer of –3.
Example Question #1 :How To Find Patterns In Exponents
Ifand, then what is?
We use two properties of logarithms:
So
Example Question #1 :Pattern Behaviors In Exponents
Evaluate:
, hereand, hence.
Example Question #1 :How To Find Patterns In Exponents
Solve for
None of the above
=
which means
Example Question #12 :Pattern Behaviors In Exponents
Which of the following statements is the same as:
Remember the laws of exponents. In particular, when the base is nonzero:
An effective way to compare these statements, is to convert them all into exponents with base 2. The original statement becomes:
This is identical to statement I. Now consider statement II:
Therefore, statement II is not identical to the original statement. Finally, consider statement III:
which is also identical to the original statement. As a result, only I and III are the same as the original statement.
Example Question #131 :Exponents
Write in exponential form:
Using properties of radicals e.g.,
we get
Example Question #131 :Exponents
Write in exponential form:
Properties of Radicals