Mathematics from zero
Powers and roots: free-recall review
Retrieval beats re-reading. For each prompt, say or write a full answer from memory before you open the model answer — the effort of recalling is what fixes the idea in place.
Reconstruct the unit’s core ideas — what an exponent counts, why the power 0 is 1, how powers of ten and zeros line up, scientific form, and square roots as the backwards question — without looking back at the lessons.
- 01What does an exponent count, and why is reading 2³ as 6 wrong?
- 02Why does any (nonzero) base raised to the power 0 equal 1?
- 03Why does the exponent of a power of ten equal its number of zeros?
- 04What is scientific form, and how do you write 50000 in it?
- 05What does a square root ask, and how does it relate to squaring?
- 06Which numbers are perfect squares, and how do you estimate the root of a number that is not one?
If you could rebuild each answer from memory, you hold the unit’s spine: an exponent counts copies of the base (never a factor), the power 0 is forced to 1 by the step-down pattern, a power of ten’s exponent is its zero count, scientific form packs a big number into a leading digit times a power of ten, and the square root runs squaring backwards — exact on perfect squares, trapped between neighbours otherwise.