All SAT Math Resources
Example Questions
Example Question #11 : Exponents
If , then which of the following is equivalent to ?
6^4
6^8
6^7
6^6
We can break up the equation into two smaller equations involving only x and y. Then, once we solve for x and y, we can find the value of .
Example Question #12 : Exponents
If which of the following must be true?
I.
II.
III.
III
I
II
None
All
None
must be negative because it has an odd power and and have even powers above. But and could be positive or negative, so none of the scenarios has to be true.
Example Question #11 : Exponents
Hence the correct answer will be
Example Question #12 : Exponents
Solve for :
If
Then
and
Hence
Example Question #12 : Exponents
(x3y6z)(x2yz3)
The paraentheses are irrelevant. Rearrange to combine like terms.
x3x2y6y1z1z3
When you multiply variables with exponents, simply add the exponents together.
x3+2 y6+1 z1+3
x5y7z4
Example Question #11 : Exponents
If an original bacteria colony contains six organisms, and triples every hour, how many organisms are there after 7 hours?
To find the answer we can apply the equation of population where is the number of hours.
Example Question #12 : Exponents
Simplify:
Use the distributive property: . When we multiply variables with exponents, we keep the same base and add the exponents:
Example Question #13 : Exponents
Simplify:
We cannot combine with , so .
Example Question #16 : Exponents
If , then what is the value of ?
c4 is equal to (c2)(c2).
We know c2 = 15. Plugging in this value gives us c4 = (15)(15) = 225.
Example Question #17 : Exponents
If and are nonzero numbers such that , which of the following is equivalent to ?
For this problem, we need to make use of the property of exponents, which states that (xy)z = xyz.
We are given a2 but are asked to find a6.
Let's raise both sides of the equation to the third power, so that we will end up with a6 on the left side.
(a2)3 = (b3)3
Now, according to the property of exponents mentioned before, we can multiply the exponents.
a(2*3) = b(3*3)
a6 = b9
The answer is b9.