Let me work through this problem step by step.
The worksheet asks to fill in the values for powers of numbers from 1 to 10, both positive and negative bases, all squared (raised to the power of 2).
Then question 2 asks if (-5)² and -5² are the same thing.
Let me calculate each:
1² = 1
(-1)² = (-1) × (-1) = 1
2² = 4
(-2)² = (-2) × (-2) = 4
3² = 9
(-3)² = (-3) × (-3) = 9
4² = 16
(-4)² = (-4) × (-4) = 16
5² = 25
(-5)² = (-5) × (-5) = 25
6² = 36
(-6)² = (-6) × (-6) = 36
7² = 49
(-7)² = (-7) × (-7) = 49
8² = 64
(-8)² = (-8) × (-8) = 64
9² = 81
(-9)² = (-9) × (-9) = 81
10² = 100
(-10)² = (-10) × (-10) = 100
Now for question 2: Is (-5)² and -5² the same thing?
(-5)² means (-5) × (-5) = 25
-5² means -(5²) = -(25) = -25
So they are NOT the same thing. (-5)² = 25 while -5² = -25.
Let me verify my calculations once more:
- All squares of integers from 1-10 are correct
- All squares of negative integers from -1 to -10 are correct (since negative times negative equals positive)
- The distinction between (-5)² and -5² is a classic order of operations issue
Final Answer:
1.
1² = 1, (-1)² = 1
2² = 4, (-2)² = 4
3² = 9, (-3)² = 9
4² = 16, (-4)² = 16
5² = 25, (-5)² = 25
6² = 36, (-6)² = 36
7² = 49, (-7)² = 49
8² = 64, (-8)² = 64
9² = 81, (-9)² = 81
10² = 100, (-10)² = 100
2. No, (-5)² and -5² are not the same thing.
(-5)² = 25
-5² = -25
Parent Tip: Review the logic above to help your child master the concept of 8th grade pre algebra worksheet.
