Answer
a) negative (-)
b) positive (+)
c) negative (-)
d) negative (-)
e) positive (+)
f) negative (-)
Work Step by Step
Note: When a negative number is taken to an even power, the result is positive, and when it is taken to an odd power, the result is negative.
a) Since b is a negative number, and it is taken to an odd power, the result will still be negative.
b) Since b is a negative number, and it is taken to an even power, the result will be positive.
c) Since a is positive, b squared is a positive number (a negative number taken to an even power), and c is a negative number (a negative number taken to an odd power), the result is a positive number times a positive number times a negative number, which is a negative number (for example, $3\times 4\times-5$ is a negative number.)
d) Since b is negative, and a is positive, the result of $b - a$ is negative. This negative number is taken to an odd power, which makes the result negative.
e) As stated in part d), $b - a$ is negative. Since it is taken to an even power, it is positive.
f) Since a is a positive number, a cubed is also positive. Since c is a negative number, c cubed is negative. Therefore, when multiplied together, the product is negative. Both b to the sixth power and c to the sixth power are both negative, so when multiplied together, the result is positive. When the positive numerator is divided by the negative denominator, the result is negative.
