Mathematics from zero
Powers and roots: multiple-choice review
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.