Calculator Skills
Powers, Roots and Reciprocals
Knowing the power, root and reciprocal keys saves time and avoids the errors that come from long manual working.
Find the right keys before the exam
Every scientific calculator has keys for squares, general powers, square roots, general roots and reciprocals, but their labels differ by model. Learn where they are on your own calculator well before the exam, not during it.
A worked keystroke sequence for powers and roots
- For 2.5³, press 2.5, then the power key (x▪ or ^ ), then 3, then = . The display reads 15.625.
- For the fourth root of 16, use the general root key: press 4, the root key, then 16, then = . The display reads 2.
- For a reciprocal such as 1 ÷ 8, press 8 then the reciprocal key x⁻¹, then = . The display reads 0.125.
- Each of these is one keystroke sequence rather than a long chain of manual multiplication, so there is far less room for a slip.
Check a root by reversing it
A root and a power undo each other, which gives you a free check. If you claim the fourth root of 16 is 2, raise 2 to the fourth power: 2⁴ = 16, so it holds.
If you find a cube root of 15.625 as 2.5, cube it: 2.5³ = 15.625. When the reverse operation lands back on the original number, your root is right; when it does not, you have found the error before the marker does.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How do I enter a cube root or a fourth root?
Most scientific calculators have a general root key where you enter the index first and the number second, so the fourth root of 16 is 4, root key, 16, equals, giving 2. Some models also have a dedicated cube-root key.
Find these keys and practise them before the exam so you are not hunting during the paper.
What does the x⁻¹ key actually do?
It gives the reciprocal, one divided by the number. Pressing 8 then x⁻¹ returns 0.125, the same as 1 ÷ 8.
It is handy for gradients of perpendicular lines and for rearranging formulas, since the reciprocal of a fraction simply flips it: the reciprocal of 3/4 is 4/3.
My power answer looks far too big or too small, what happened?
Check that you used the general power key and typed the correct index, and that the base did not accidentally include a sign or bracket. Confusing the square key with the power key, or slipping between an index of 2 and 3, is the usual cause.
Reversing the operation is the quickest way to confirm the value.