Even and Odd Powers: Effects on the Sign
_x_ is a positive odd number, and _y_ is a positive even number.
| Quantity A | Quantity B |
|----|----|
| (–_x_)_y_ | (–_y_)_x_ |
Correct.
Quantity A is a negative odd number, –_x_, raised to an even exponent, _y_. Since any value raised to an even exponent is positive, you know that Quantity A is greater than 0.
Quantity B is a negative even number, –_y_, raised to an odd exponent, _x_. Any value raised to an odd exponent will maintain its sign, so Quantity B is negative.
Any number greater than 0 will be greater than a negative number, so Quantity A is greater.
Incorrect.
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Do not make assumptions about the values of the two variables. Since you do not know the value of either _x_ or _y_, you only need to pay attention to the sign of each quantity.
Incorrect.
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The two bases both have the same sign, but one exponent is even and the other is odd. This means that the resulting values will have different signs. The quantities cannot be equal.
Incorrect.
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You do not need any additional information about the values of _x_ and _y_. Follow the rules for even and odd exponents, keeping track of the sign of each quantity.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
