IGCSE Maths Indices and Standard Form Questions and Answers
Indices and Standard Form questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then cover each solution and redo it yourself.
Laws of indices (integer powers): Simplifying expressions using the rules for multiplying, dividing and raising powers.
Indices 1: Laws of positive-integer indices.
Indices 2: Fractional and negative indices.
Standard Form 1: Writing numbers in a×10^n form.
Standard Form 2: Multiplying and dividing standard-form numbers.
Indices and Standard Form worked examples
Worked example 1: Laws of indices
Simplify \(x^7\times x^4\div x^3\).
Solution
Multiplying: add the powers, \(x^{7+4}=x^{11}\).
Dividing: subtract the powers, \(x^{11-3}=x^{8}\).
Answer: \(x^8\)
Tip: Only add or subtract powers when the base is the same.
Worked example 2: Powers of powers
Simplify \((x^4)^3\times x^{-5}\).
Solution
\((x^4)^3=x^{12}\).
\(x^{12}\times x^{-5}=x^{7}\).
Answer: \(x^7\)
Tip: A power of a power: multiply the indices.
Worked example 3: Fractional indices
Evaluate \(32^{\frac{3}{5}}\).
Solution
The denominator 5 means fifth root: \(\sqrt[5]{32}=2\).
Then cube: \(2^3=8\).
Answer: 8
Tip: Root first, then power, keeps the numbers small.
Worked example 4: Converting to standard form
Write (a) 0.000 070 3 in standard form (b) \(4.6\times10^{6}\) as an ordinary number.
Solution
(a) Move the decimal point 5 places right to get 7.03, so \(7.03\times10^{-5}\).
(b) Move the decimal point 6 places right: 4 600 000.
Answer: (a) \(7.03\times10^{-5}\) (b) 4 600 000
Tip: Small numbers have negative powers of 10.
Worked example 5: Calculating in standard form
Work out \((7\times10^{5})\times(6\times10^{-2})\), giving your answer in standard form.
Solution
Multiply the numbers: \(7\times6=42\).
Add the powers: \(10^{5+(-2)}=10^{3}\).
\(42\times10^3=4.2\times10^{4}\).
Answer: \(4.2\times10^{4}\)
Tip: The first number must be between 1 and 10.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Which Edexcel IGCSE Maths papers test indices and standard form?
Either Higher tier paper, 1H or 2H, can test indices and standard form: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more indices and standard form questions?
In the IGCSE student hub: Unit 1 (Number) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
IGCSE Math Revision