Multiplication with Indices
When multiplying indices, you simply add the powers. For example, 2a² x a³ = 2a(²+3) = 2a⁵.
Negative Indices/Powers
This involves negative reciprocals. For example, 3⁻² = 1/3² = 1/9.
Working with Fractions
Negative powers mean flip fractions. Leave it in its simplest form or change it to a mixed number. For example, -3/13 = -1/3.
Fractional Powers
You need to change a^(1/4) = 9√a⁴.
Division with Indices
When dividing indices, you simply subtract the powers. For example, 36⁶⁸ ÷ 6⁴³ = 96(8-3) = 96³.
Harder Examples
For harder examples like 4x²³, it can be solved step by step to get the result.
Algebra
Using algebra, the same principles apply as with numbers. Solve each side first and then put together the pieces to find the solution.
Working Backwards
If you have a decimal, turn it into a fraction before solving. For example, (25)³/2 = (√5)² = (√5)³.
Fractional Powers with Negative Indices
When dealing with negative indices in fractional powers, you need to put it as a fraction and use the rule a^n = √a to solve the denominator.
Calculate division with indices using the provided examples and solutions.
Understand how to work with negative and fractional powers using the laws of indices.
Practice calculating with indices by answering the provided questions. This will help you get familiar with the rules of indices and how to apply them.
Use the provided indices worksheet to apply the rules of indices and practice various problems to strengthen your understanding.
