Let’s solve each exponent problem step by step. Remember:
- A
positive exponent means multiply the base by itself that many times.
- A
negative exponent means take the reciprocal (1 over) of the base raised to the positive exponent.
- If the base is negative and the exponent is even → result is positive.
- If the base is negative and the exponent is odd → result is negative.
We’ll go one by one.
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1) (-8)²
= (-8) × (-8) = 64 → *even power, so positive*
2) (4)³
= 4 × 4 × 4 = 64
3) (10)⁻²
= 1 / (10²) = 1/100 = 0.01
4) (-6)⁻
First, ignore sign for now: 6⁴ = 1296
Since exponent is even, (-6)⁴ = 1296 → then reciprocal: 1/1296
5) (-9)⁻³
Exponent is odd → (-9)³ = -729 → reciprocal: 1/(-729) = -1/729
6) (-10)²
= (-10) × (-10) = 100 → even power → positive
7) (12)⁻²
= 1/(12²) = 1/144
8) (6)⁴
= 6×6×6×6 = 36×36 = 1296
9) (3)⁴
= 3×3×3×3 = 81
10) (-2)⁻⁷
Exponent is odd → (-2) = -128 → reciprocal: 1/(-128) = -1/128
11) (-2)⁻⁸
Exponent is even → (-2)⁸ = 256 → reciprocal: 1/256
12) (-3)⁻⁴
Even exponent → (-3)⁴ = 81 → reciprocal: 1/81
13) (5)²
= 25
14) (2)³
= 8
15) (-12)²
Even exponent → (-12)² = 144 → reciprocal: 1/144
16) (-3)⁻⁵
Odd exponent → (-3) = -243 → reciprocal: -1/243
17) (7)²
= 49
18) (-4)⁻⁴
Even exponent → (-4)⁴ = 256 → reciprocal: 1/256
19) (9)⁻³
= 1/(9³) = 1/729
20) (8)⁻³
= 1/(8³) = 1/512
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Final Answer:
1) 64
2) 64
3) 1/100 or 0.01
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) 1/256
19) 1/729
20) 1/512
Parent Tip: Review the logic above to help your child master the concept of mathematics grade 7 worksheet.
