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ACARA AC9M9A01, Exponent laws with variables

Year 9 · Algebra

Apply the index laws to numerical expressions with integer exponents and extend them to expressions with variables.

Below are free printable maths worksheets that support AC9M9A01. Print them as PDFs, or generate a fresh one. Every maths answer key is computed in code, so it is never wrong.

Teaching guide

What students learn

Apply the index laws to numerical expressions with integer exponents and extend them to expressions with variables.

How to teach it

Extend the index laws to negative and zero exponents with numbers first, then to variables, justifying each step from the meaning of a power.

Worked example
Simplify: 2^4 x 2^4 (write as 2^?)
Answer: 2^8
Why: 2^(4+4) = 2^8

Generated and checked in code, so it is correct.

Watch out for

Mishandling negative exponents (a negative power means a reciprocal, not a negative number), and adding exponents when the bases differ.

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More Year 9 Algebra codes: AC9M9A02 · AC9M9A03 · AC9M9A04 · AC9M9A05 · AC9M9A06
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Australian Curriculum content descriptions (c) ACARA, used under CC BY 4.0. Descriptions are paraphrased. See australiancurriculum.edu.au.