evaluate -a^n when a=3 and n=2,3,4 and 5. Now evaluate (-a)^n when a=3 and n=2,3,4 and 5. Based on this sample, does it appear that -a^n=(-a)^n? If not, state the relationships, if any, between -a^n and (-a)^n.
THANK YOU!!
-(a)^n will always be negative.
(-a)^n will be positive for the even powers.
To evaluate -a^n when a = 3 and n = 2, 3, 4, and 5, we can substitute these values into the expression.
1. For n = 2:
-a^2 = -(3^2) = -9
2. For n = 3:
-a^3 = -(3^3) = -27
3. For n = 4:
-a^4 = -(3^4) = -81
4. For n = 5:
-a^5 = -(3^5) = -243
Now, let's evaluate (-a)^n when a = 3 and n = 2, 3, 4, and 5.
1. For n = 2:
(-a)^2 = (-3)^2 = 9
2. For n = 3:
(-a)^3 = (-3)^3 = -27
3. For n = 4:
(-a)^4 = (-3)^4 = 81
4. For n = 5:
(-a)^5 = (-3)^5 = -243
From the evaluations above, we can see that -a^n is not equal to (-a)^n. When n is even, changing the sign of "a" has no effect on the result. However, when n is odd, changing the sign of "a" affects the result.
The relationship between -a^n and (-a)^n is as follows:
- If n is even, -a^n = (-a)^n.
- If n is odd, -a^n = -(-a)^n.
In summary, (-a)^n and -a^n are not equal in general, and the relationship between them depends on the parity of n.