Powers and roots: multiple-choice review
Multiple-choice review across the powers unit — what an exponent counts, powers of ten and their zeros, the power 0, and square roots as the backwards question.
Six questions that reach across the whole unit. Each one targets a place where it is easy to slip — counting the exponent as a factor, miscounting zeros, or mixing up squaring with halving. Reason each one out before you pick.
Confirm you can read an exponent as a count of factors, turn powers of ten into zeros and back, handle the power 0, and run a square root backwards from a perfect square — the synthesis the three lessons built toward.
What is 2⁴, and what does the exponent 4 actually tell you to do?
Without multiplying it out, how many zeros does 10⁷ have, and why?
A colleague claims 9⁰ = 0 because raising to the power 0 means 'no copies, so nothing'. What is the value, and why?
Written as a small number times a power of ten, what is 70000?
What number does √64 ask for, and what is it?
√50 is not a whole number. Between which two whole numbers does it fall, and on which side?
The through-line across the unit is one habit: read the exponent as a count of factors, never a factor itself. That single idea handles powers (2⁴ is four 2s), powers of ten (the exponent is the zero count), and the power 0 (the step-down pattern forces 1). Square roots run the same machine backwards — what number, squared, gives this? — landing exactly on perfect squares and trapping every other root between the two nearest ones.
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