GRE Math : Exponents
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Example Questions
Example Question #6 : Exponential Operations
If 
Rewrite the term on the left as a product. Remember that negative exponents shift their position in a fraction (denominator to numerator).
The term on the right can be rewritten, as 27 is equal to 3 to the third power.
Exponent rules dictate that multiplying terms allows us to add their exponents, while one term raised to another allows us to multiply exponents.
We now know that the exponents must be equal, and can solve for 
Example Question #81 : Exponential Operations
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 #12 : Exponential Operations
Simplify 
Start by simplifying each individual term between the plus signs. We can add the exponents in 
Example Question #1551 : Gre Quantitative Reasoning
Simplify 
First, simplify 
Then simplify 
This gives us 
Example Question #14 : Exponential Operations
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 #15 : Exponential Operations
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)
3^21
4^4
None of the other answers
3^3 * 4^21 * 5
3^3 * 4^21
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 #1551 : Gre Quantitative Reasoning
Quantitative Comparison
Quantity A: 64 – 32
Quantity B: 52 – 42
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.
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 relationship cannot be determined from the information given.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
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.
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