Multiply two powers and the exponents add; raise a power to a power and they multiply. These free printable worksheets show a line where the wrong one of those two was used, and ask which answer is correct.
The two laws are the most confusable pair in early algebra, and the reason is that neither is memorable on its own — they are memorable against each other. A sheet that practices only one teaches a child to apply whichever they last saw, which is why both appear here on the same page.
Why this sheet works
The wrong answers are the real confusions rather than arithmetic slips: exponents multiplied when they should be added, subtracted instead of added, the two bases added as well as their powers, the product turned into a sum. Each one is a rule a student has actually reached for.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Read each line of working and choose the answer that is correct.
1Spot the mistake: (x³)² · x² = x¹². Which answer is right?x¹²x⁶x⁷x⁸Why?
2On Priya's paper: x³ · x³ ÷ x² = x². Which line should replace it?x²x⁴x⁷x⁸Why?
3Ben wrote (x³)⁴ · x² = x⁹. Which is correct?x¹²x²⁴x⁹x¹⁴Why?
4On Ana's paper: x⁴ · x³ ÷ x² = x⁹. Which line should replace it?x⁵x¹⁰x⁹x³Why?
Algebra reasoning · Exponent lawsAnswer key
1. (x³)² · x² = x⁸, not x¹² (the last power was multiplied in as well as the first two)2. x³ · x³ ÷ x² = x⁴, not x² (the second power was taken away and the third one added)3. (x³)⁴ · x² = x¹⁴, not x⁹ (the stacked powers were added where they should be multiplied)4. x⁴ · x³ ÷ x² = x⁵, not x⁹ (the dividing step added its power instead of taking it away)
