Indices and Surds — NSW Year 10 Core Maths
Index laws, zero and negative indices, and scientific notation for Year 10. Four subtopics and 80 practice questions, each with a worked solution, aligned to NESA MA5-IND-C-01, MA5-IND-P-01 and MA5-MAG-C-01.
Indices and Surds in NSW Year 10 Core
Indices give a short way to write repeated multiplication. In Year 10 Core, students use the multiplication, division and power laws, work with zero and negative indices, and write very large and very small numbers in scientific notation. Surds and fractional indices are studied in Year 10 Advanced.
The four subtopics below run in that order, from the index laws to scientific notation. Indices and Surds is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Number and Algebra strand (NESA outcomes MA5‑IND‑C‑01, MA5‑IND‑P‑01 and, for scientific notation, MA5‑MAG‑C‑01). The index laws are needed for exponential graphs and Stage 6 maths.
Subtopics
Indices and Surds: common questions
What are the index laws for multiplying and dividing?
When you multiply powers of the same base, add the indices. When you divide, subtract them. So \(a^5 \times a^3 = a^8\) and \(a^5 \div a^3 = a^2\).
How do you write a number in scientific notation?
Write it as a number from 1 up to, but not including, 10, multiplied by a power of 10. For example, \(45\,000 = 4.5 \times 10^4\) and \(0.0032 = 3.2 \times 10^{-3}\).
What does a negative index mean?
A negative index means the reciprocal of the positive power: \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\). Any non-zero number to the power 0 equals 1.
Which NESA outcomes cover indices in Year 10 Core?
The index laws and the zero index come under MA5‑IND‑C‑01, and negative indices with pronumerals under MA5‑IND‑P‑01. Scientific notation is part of MA5‑MAG‑C‑01, Numbers of any magnitude.
Why learn indices?
Scientific notation is how scientists write huge and tiny measurements. The index laws are also the basis of exponential growth and of Stage 6 maths.