All SAT Math Resources
Example Questions
Example Question #21 : How To Multiply Exponents
If and are positive integers and , what is the value of ?
The question tells us that 22a ( 22b )= 16.
We can rewrite 16 as 24, giving us 22a ( 22b )= 24.
When terms with the same base are multipled, their exponents can be added:
2(2a +2b) = 24
Since the base is the same on both sides of the equation, we can equate the exponents:
2a +2b = 4
2(a + b) = 4
a + b = 2
Example Question #1 : How To Multiply Exponents
(b * b4 * b7)1/2/(b3 * bx) = b5
If b is not negative then x = ?
–2
–1
1
7
–2
Simplifying the equation gives b6/(b3+x) = b5.
In order to satisfy this case, x must be equal to –2.
Example Question #1563 : Gre Quantitative Reasoning
If〖7/8〗n= √(〖7/8〗5),then what is the value of n?
25
2/5
√5
1/5
5/2
5/2
7/8 is being raised to the 5th power and to the 1/2 power at the same time. We multiply these to find n.
Example Question #2 : How To Multiply Exponents
Simplify: (x3 * 2x4 * 5y + 4y2 + 3y2)/y
None of the other answers
10x7 + 7y3
10x7 + 7y
10x11 + 7y3
10x7y + 7y2
10x7 + 7y
Let's do each of these separately:
x3 * 2x4 * 5y = 2 * 5 * x3 * x4 * y = 10 * x7 * y = 10x7y
4y2 + 3y2 = 7y2
Now, rewrite what we have so far:
(10x7y + 7y2)/y
There are several options for reducing this. Remember that when we divide, we can "distribute" the denominator through to each member. That means we can rewrite this as:
(10x7y)/y + (7y2)/y
Subtract the y exponents values in each term to get:
10x7 + 7y
Example Question #1568 : Gre Quantitative Reasoning
Compare and .
The answer cannot be determined from the information given.
To compare these expressions more easily, we'll change the first expression to have in front. We'll do this by factoring out 25 (that is, ) from 850, then using the fact that .
When we combine like terms, we can see that . The two terms are therefore both equal to the same value.
Example Question #1569 : Gre Quantitative Reasoning
Which of the following is equal to ?
is always equal to ; therefore, 5 raised to 4 times 5 raised to 5 must equal 5 raised to 9.
is always equal to . Therefore, 5 raised to 9, raised to 20 must equal 5 raised to 180.
Example Question #3 : How To Multiply Exponents
Which of the following is equal to ?
First, multiply inside the parentheses: .
Then raise to the 7th power: .
Example Question #21 : Exponential Operations
Simplify:
Remember, we add exponents when their bases are multiplied, and multiply exponents when one is raised to the power of another. Negative exponents flip to the denominator (presuming they originally appear in the numerator).
Example Question #22 : How To Multiply Exponents
Evaluate:
Can be simplified to:
Example Question #21 : Exponents
When multplying exponents, we need to make sure we have the same base.
Since we do, all we have to do is add the exponents.
The answer is .