SAT Math : SAT Mathematics
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Example Questions
Example Question #91 : Exponents
Evaluate:
When adding exponents, you want to factor out to make solving the question easier.
We have the same base so we just apply the exponent rule for multiplication to get
Example Question #92 : Exponents
Which of the following is equivalent to 
Although each base is different, we can convert them to a common base of 
We know
and
Remember to apply the power rule of exponents.
Therefore we have
We can factor out 
Example Question #93 : Exponents
Simplify:
When adding exponents, you want to factor out to make solving the question easier.
We can factor out 
Now we can add exponents and therefore our answer is
Example Question #2281 : Sat Mathematics
Given 
7
5
9
3
11
7
Express 
Then 
Using the properties of exponents, 
Therefore, 
Example Question #2 : How To Add Exponents
If 
Since we have two 
For 
So we have 
Or
Divide this by 
Thus 
*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.
Example Question #1 : How To Subtract Exponents
If m and n are integers such that m < n < 0 and m2 – n2 = 7, which of the following can be the value of m + n?
I. –5
II. –7
III. –9
II only
I, II and III only
I and II only
I only
II and III only
II only
m and n are both less than zero and thus negative integers, giving us m2 and n2 as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.
Example Question #2 : How To Subtract Exponents
To simplify, we can rewrite the numerator using a common exponential base.
Now, we can factor out the numerator.
The eights cancel to give us our final answer.
Example Question #3 : How To Subtract Exponents
Simplify the following expression:
The correct answer can be found by subtracting exponents that have the same base. Whenever exponents with the same base are divided, you can subtract the exponent of the denominator from the exponent of the numerator as shown below to obtain the final answer:
You do not do anything with the y exponent because it has no identical bases.
Example Question #3 : How To Subtract Exponents
Solve:
Subtract the denominator exponent from the numerator's exponent, since they have the same base.
Example Question #11 : Exponential Operations
Simplify: 32 * (423 - 421)
3^3 * 4^21 * 5
3^21
3^3 * 4^21
4^4
None of the other answers
3^3 * 4^21 * 5
Begin by noting that the group (423 - 421) has a common factor, namely 421. You can treat this like any other constant or variable and factor it out. That would give you: 421(42 - 1). Therefore, we know that:
32 * (423 - 421) = 32 * 421(42 - 1)
Now, 42 - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:
32 * 421(42 - 1) = 32 * 421(3 * 5)
Combining multiples withe same base, you get:
33 * 421 * 5
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