Indices and Scientific Notation — NSW Year 9 Core Maths
The index laws, zero and negative indices, scientific notation and significant figures. Eight subtopics and 160 practice questions, each with a fully worked solution, aligned to NESA outcomes MA5-IND-C-01 and MA5-MAG-C-01.
Indices and Scientific Notation in NSW Year 9
Indices are a short way of writing repeated multiplication, and the index laws turn long calculations into quick ones: \(a^m \times a^n = a^{m+n}\), \(a^m \div a^n = a^{m-n}\) and \((a^m)^n = a^{mn}\). In Year 9 Core students apply these laws to pronumerals, find out why \(x^0 = 1\) and what a negative index means, then use powers of ten to write very large and very small numbers in scientific notation.
The eight subtopics below cover multiplying and dividing, the zero index, the power of a power, a summary of the laws, negative indices and mixed questions, then scientific notation and significant figures. Indices and Scientific Notation is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Number and Algebra strand. The index laws come under NESA outcome MA5‑IND‑C‑01, and scientific notation and significant figures under MA5‑MAG‑C‑01. Index laws are used again with surds and fractional indices in Year 10, and scientific notation is everywhere in science.
Subtopics
Indices and Scientific Notation: common questions
What are the index laws?
When multiplying powers of the same base, add the indices: \(a^m \times a^n = a^{m+n}\). When dividing, subtract them: \(a^m \div a^n = a^{m-n}\). For a power of a power, multiply them: \((a^m)^n = a^{mn}\). Any non-zero base to the power zero is \(1\).
Why is any number to the power zero equal to 1?
Divide a power by itself. By the division law \(x^4 \div x^4 = x^{4-4} = x^0\), but anything divided by itself is \(1\), so \(x^0\) must equal \(1\).
What does a negative index mean?
A negative index means the reciprocal of the positive power. For example, \(3^{-4} = \frac{1}{3^4} = \frac{1}{81}\), and \(2b^{-3} = \frac{2}{b^3}\).
How do you write a number in scientific notation?
Move the decimal point until the first part is at least \(1\) and less than \(10\), then multiply by the power of ten that undoes the move. So \(584\,000 = 5.84 \times 10^5\) and \(0.057 = 5.7 \times 10^{-2}\).
Which NESA outcomes cover indices and scientific notation in Year 9?
The index laws with positive and zero indices, and what a negative index means for a number base, are Stage 5 Core content under MA5‑IND‑C‑01. Scientific notation and rounding to significant figures come under MA5‑MAG‑C‑01.