GRE Math : Exponential Operations
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Example Questions
Example Question #1551 : Gre Quantitative Reasoning
If 
Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.
Example Question #53 : Exponents
Simplify 
Start by simplifying each individual term between the plus signs. We can add the exponents in 
Example Question #51 : Exponents
Simplify 
First, simplify 
Then simplify 
This gives us 
Example Question #6 : How To Add Exponents
If 
To attempt this problem, note that 
Now note that when multiplying numbers, if the base is the same, we may add the exponents:
This can in turn be written in terms of nine as follows (recall above)
Example Question #52 : Exponents
If 
When dealing with exponenents, when multiplying two like bases together, add their exponents:
However, when an exponent appears outside of a parenthesis, or if the entire number itself is being raised by a power, multiply:
Example Question #1 : How To Subtract Exponents
Simplify: 32 * (423 - 421)
None of the other answers
3^3 * 4^21 * 5
4^4
3^3 * 4^21
3^21
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
Example Question #1 : How To Subtract Exponents
Quantitative Comparison
Quantity A: 64 – 32
Quantity B: 52 – 42
The relationship cannot be determined from the information given.
Quantity A is greater.
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.
Example Question #1561 : Gre Quantitative Reasoning
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
Quantity A is greater.
The first thing to note is the relationship between (–b) and (1 – b):
(–b) < (1 – b) because (–b) + 1 = (1 – b).
Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.
Raising a negative number to an odd power produces another negative number.
Thus (–b)a < (1 – b)a < 0.
Example Question #1 : How To Multiply Exponents
(b * b4 * b7)1/2/(b3 * bx) = b5
If b is not negative then x = ?
–1
1
7
–2
–2
Simplifying the equation gives b6/(b3+x) = b5.
In order to satisfy this case, x must be equal to –2.
Example Question #2 : How To Multiply Exponents
If〖7/8〗n= √(〖7/8〗5),then what is the value of n?
1/5
5/2
2/5
25
√5
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.
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