Why does my child think 3x⁻² × 5x⁶ = 15x⁸?
Your child leaves out the minus sign of a negative index, such as giving 3x⁻² × 5x⁶ as 15x⁸ instead of 15x⁴.
Why children do it
Adding the indices is the right rule, so it feels finished. But the −2 is a negative number, and adding it takes 2 away: −2 + 6 = 4, so the answer is 15x⁴. Writing the indices out with their signs before adding them catches it.
How to help at home
Ask them to write the indices out with their signs, -2 + 6, before working it out.
The right way
Simplify: 3x⁻² × 5x⁶
- 15 × x⁻² × x⁶Multiply the numbers: 3 × 5 = 15.
- 15x⁴Add the indices: -2 + 6 = 4.
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