Today is rung 5 of 10 on this topic
Exponent rules and scientific notation
Can do: Applies exponent laws including zero and negative exponents, and computes with scientific notation.
Why it matters
Exponents underpin scientific measurement, growth and everything in high-school science. Negative exponents are the usual sticking point.
What it looks like when it's wobbly
Thinks a negative exponent makes the number negative, and adds exponents when multiplying the bases too.
⏱️ Two-minute check
"Simplify 2³ × 2⁵. What is 5⁻²? Write 0.00042 in scientific notation."
Solid looks like: 2⁸, 1/25, and 4.2 × 10⁻⁴.
The full activity for this topic · 20 minutes
Build the Rules from the Pattern
- 1Write 2⁵ = 32, 2⁴ = 16, 2³ = 8 and continue the halving down through 2⁰ and into negatives.
- 2The rules emerge from the pattern instead of being announced.
- 3Expand 2³ × 2⁵ fully to see why the exponents add.
- 4Practise scientific notation on real quantities: the distance to the sun, the size of a cell.
- 5Compare two very different magnitudes and say how many times bigger one is.
If it's too hard
Positive exponents and the multiplication rule only.
If it's too easy
Operations in scientific notation, including division and adding unlike magnitudes.
Say this
"Keep halving. What has to come after 2⁰? The pattern doesn't stop just because it gets weird."