Mastering Indices & Powers
Mathematics
Year 9
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About This Worksheet
A worksheet covering Indices & Powers for Year 9 students, focusing on understanding and applying the laws of indices.
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Mastering Indices & Powers
Subject: MathematicsGrade: Year 9
Name:
Date:
Untitled Worksheet
Grade Year 9
A
Introduction
Review the laws of indices: for any numbers a and b, and integers m and n, the laws include: a^m * a^n = a^{m+n}, (a^m)^n = a^{m*n}, and a^{-n} = 1 / a^n. Use these to simplify and evaluate expressions.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Simplify: 2^3 * 2^4
[2 marks]2.
Calculate: (3^2)^4
[2 marks]3.
Express 125 as a power of 5.
[2 marks]4.
Simplify: 5^2 * 5^{-3}
[2 marks]5.
Evaluate: 2^5 / 2^2
[2 marks]6.
Simplify: (4^3)^2
[2 marks]7.
Express 1/81 as a power of 3.
[2 marks]8.
Simplify: 7^0
[2 marks]9.
Calculate: 10^3 * 10^{-2}
[2 marks]10.
Simplify: (2^4)^3
[2 marks]11.
Challenge: A bacteria culture starts with 2^3 bacteria. Each hour, the bacteria multiply by a factor of 2. Write an expression for the number of bacteria after n hours and evaluate it when n=5.
[4 marks]12.
Real-world Application: An engineer is designing a circuit with resistors. The resistance is proportional to a power of 2, and the total resistance R is given by R = 2^{k}, where k is a variable. If the engineer needs a resistance of 64 ohms, what value of k is required?
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet