Exponential Operations
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GRE Quantitative Reasoning › Exponential Operations
If 
Cannot be determined
Explanation
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
Quantitative Comparison
Quantity A: 64 – 32
Quantity B: 52 – 42
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
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.
Quantity A:
(0.5)3(0.5)3
Quantity B:
(0.5)7
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:
xaxb = xa+b
This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6
Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.
Thus, (0.5)6 > (0.5)7
If
Cannot be determined
Explanation
Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.
Quantity A:
(0.5)3(0.5)3
Quantity B:
(0.5)7
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:
xaxb = xa+b
This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6
Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.
Thus, (0.5)6 > (0.5)7
Quantitative Comparison
Quantity A: 64 – 32
Quantity B: 52 – 42
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Explanation
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.
If 
Explanation
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:
Indicate whether Quantity A or Quantity B is greater, or if they are equal, or if there is not enough information given to determine the relationship.
Quantity A:
Quantity B:
Quantity B is greater.
Quantity A is greater.
The quantities are equal.
The relationship cannot be determined from the information given.
Explanation
By using exponent rules, we can simplify Quantity B.
Also, we can simplify Quantity A.
Since n is positive,
Simplify
None
Explanation
Divide the coefficients and subtract the exponents.
(b * b4 * b7)1/2/(b3 * bx) = b5
If b is not negative then x = ?
–2
–1
7
1
Explanation
Simplifying the equation gives b6/(b3+x) = b5.
In order to satisfy this case, x must be equal to –2.