Using Calculator for Indices

1Summary 重點摘要

Learn how to use calculator to calculate powers and scientific notation, practical for exams.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: The power keyScientific calculators have a key labelled ^ or xʸ for computing powers. To find 2³: press 2, then ^ or xʸ, then 3, then =, and the display shows 8. The four actions correspond to base, power key, index and equals. Why learn this key? Manual computation of indices is slow and error-prone, while the calculator gives an exact value at once. A common mistake is pressing the index before the base, producing 3² = 9, a completely different answer.
2. Step 2: Entering negative indicesNegative indices use the same power key, but the index should be enclosed in brackets with the minus sign inside. To find 2⁻³: press 2, ^, (, −3, ) and finally =, giving 0.125, which is 18. Why brackets? Some calculators read the minus sign after ^ as subtraction and perform it first, producing a wrong result; brackets force −3 to be treated as one complete index. A common mistake is omitting the brackets and pressing − 3 directly; make bracketing a habit.
3. Step 3: Scientific notation with the EXP keyFor scientific notation, use the EXP (or ×10ˣ) key to enter powers of ten in one action. To enter 3 × 10⁵: press 3, then EXP, then 5, and the calculator treats it as 300000 without typing five zeros. The key turns the mantissa and the power of ten into a single number ready for further arithmetic. A common mistake is keying 3, ×, 10, ^, 5 separately; the result matches here, but with a large index such as 6.02 × 10²³ errors become likely.
4. Step 4: The importance of bracketsBrackets decide the order of operations for repeated powers and must not be omitted. For (2³)²: with correct brackets, (2³)² = 2⁶ = 64; without them, many calculators read 2^(3²), giving 2⁹ = 512, a huge difference. The power operation is right-associative, so the index is evaluated first. This matters because exam questions often use the form (aᵐ)ⁿ, and a wrong order loses all marks. A common mistake is dropping the brackets; decide their position before keying in.
5. Step 5: Checking the answerAfter every calculation, estimate whether the answer is reasonable. For 10³ the answer should be 1000; if the display shows 100, a key was pressed wrongly. 2⁰ should give 1, and 5⁻² should give a decimal between 0 and 1, namely 0.04. Why check? The calculator executes exactly what is entered and gives no warning; only by checking the order of magnitude and the sign can errors be caught. A common mistake is copying a wrong value into the answer without checking.
6. Step 6: Preparation before the examBefore the exam, become fully familiar with the calculator you are allowed to use: brands differ in key positions and input methods, some use ^ and some xʸ, and the negative sign is entered in different places. Practise three types in advance: positive indices such as 2¹⁰ = 1024, negative indices such as 2⁻³ = 0.125, and scientific notation such as 3 × 10⁵. Rehearsal matters because hunting for keys during the exam wastes time and raises anxiety. A common mistake is borrowing an unfamiliar model and failing basic input.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Use ^ button for powers
• Use EXP button for scientific notation
• Remember brackets for complex expressions
• Check after calculating
• Get familiar with calculator before exam