Let’s go through each problem one by one. We’re evaluating exponents — that means multiplying the base number by itself as many times as the exponent says.
Important rules to remember:
- A negative exponent means: take the reciprocal (flip the fraction) and make the exponent positive.
Example: 2⁻³ = 1/(2³) = 1/8
- If the base is negative and in parentheses, like (-5)², you multiply the negative number by itself: (-5) × (-5) = 25.
- If there are no parentheses, like -5², it means -(5²) = -25 — but in this worksheet, all bases with negatives are in parentheses, so we’re safe!
Let’s solve each:
1) (-8)² = (-8) × (-8) = 64
2) (4)³ = 4 × 4 × 4 = 64
3) (10)⁻² = 1/(10²) = 1/100
4) (-6)⁻⁴ = 1/((-6)⁴) = 1/(6×6×6×6) = 1/1296
5) (-9)⁻³ = 1/((-9)³) = 1/(-729) = -1/729
6) (-10)² = (-10) × (-10) = 100
7) (12)⁻² = 1/(12²) = 1/144
8) (6)⁴ = 6 × 6 × 6 × 6 = 1296
9) (3)⁴ = 3 × 3 × 3 × 3 = 81
10) (-2)⁻⁷ = 1/((-2)⁷) = 1/(-128) = -1/128
11) (-2)⁻⁸ = 1/((-2)⁸) = 1/256 (even power → positive)
12) (-3)⁻⁴ = 1/((-3)⁴) = 1/81
13) (5)² = 5 × 5 = 25
14) (2)³ = 2 × 2 × 2 = 8
15) (-12)⁻² = 1/((-12)²) = 1/144
16) (-3)⁻⁵ = 1/((-3)⁵) = 1/(-243) = -1/243
17) (7)² = 7 × 7 = 49
18) (-4)⁴ = (-4) × (-4) × (-4) × (-4) = 256 (even number of negatives → positive)
19) (9)⁻³ = 1/(9³) = 1/729
20) (8)⁻³ = 1/(8³) = 1/512
Double-checking a few tricky ones:
- Problem 5: (-9)⁻³ → 1 / [(-9)×(-9)×(-9)] = 1 / [-729] → correct, negative result.
- Problem 10: (-2)⁻⁷ → 1 / [(-2)^7] = 1 / [-128] → correct.
- Problem 18: (-4)^4 → four negatives multiplied: positive → 256 → correct.
All look good.
Final Answer:
1) 64
2) 64
3) 1/100
4) 1/1296
5) -1/729
6) 100
7) 1/144
8) 1296
9) 81
10) -1/128
11) 1/256
12) 1/81
13) 25
14) 8
15) 1/144
16) -1/243
17) 49
18) 256
19) 1/729
20) 1/512
Parent Tip: Review the logic above to help your child master the concept of grade 8 math worksheet printable.
