GRE Math : How to subtract exponents
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Example Question #1 :How To Subtract Exponents
Simplify: 32* (423- 421)
3^3 * 4^21
None of the other answers
3^21
4^4
3^3 * 4^21 * 5
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
Quantity A is greater.
The two quantities are equal.
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 64vs 52. 64is clearly bigger. Now let's look at 32vs 42. 32is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.
Example Question #2 :How To Subtract Exponents
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.
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