Question

evaluate each of the following.
a) $(-3)^2$
b) $(-3)^3$
c) $-3^2$
d) $-(-3)^3$

Explanation:

Step1: Evaluate \((-3)^2\)

The exponent applies to the base \(-3\). So, \((-3)^2 = (-3) \times (-3) = 9\).

Step2: Evaluate \((-3)^3\)

The exponent applies to the base \(-3\). So, \((-3)^3 = (-3) \times (-3) \times (-3) = -27\).

Step3: Evaluate \(-3^2\)

The exponent applies to the base \(3\) first, then the negative sign. So, \(-3^2 = - (3 \times 3) = -9\).

Step4: Evaluate \(-(-3)^3\)

First, evaluate \((-3)^3 = -27\), then apply the negative sign. So, \(-(-3)^3 = - (-27) = 27\).

Answer:

a) \(9\)
b) \(-27\)
c) \(-9\)
d) \(27\)