Why does my child think 2⁻³ = −8?
Your child makes the answer negative for a negative index, such as 2⁻³ = -8.
Why children do it
A minus sign usually means a negative number, so 2⁻³ looks as if it should be negative. But following the pattern 2² = 4, 2¹ = 2, 2⁰ = 1, halving each time, gives 2⁻¹ = 1/2, then 1/4, then 1/8. So 2⁻³ is 1/8: a negative index means the reciprocal of the positive power, 1/2³.
How to help at home
Ask them to follow the pattern down: 2² = 4, 2¹ = 2, 2⁰ = 1, each one halved. What comes after 1?
The right way
Write as a fraction: 4⁻³
- 1/4³A negative index means one over.
- 1/644 cubed is 64.
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