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Understanding Fractional Indices and Their Rules for Multiplication, Division, and Powers

This guide provides a comprehensive overview of fractional indices, including the essential rules for multiplication, division, and powers. It explains the multiplication rule (am x an = am+n), the division rule (am ÷ an = am-n), and the power rule ((am)n = amn). Additionally, it introduces the concept of negative indices and unit fractions. The guide offers illustrative examples, evaluates expressions, and demonstrates how to write in index form. Furthermore, the guide includes problem-solving techniques involving equations with indices.

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Understanding Fractional Indices and Their Rules for Multiplication, Division, and Powers

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  1. Fractional Indices Multiplication Rule am x an = am+n a0 = 1 Division Rule am an = am-n Power Rule (am)n = amn Negative Index Rule Evaluate the following: Write in index form: Consider the following: So in general: 2 3 5 3 2

  2. Fractional Indices Multiplication Rule am x an = am+n a0 = 1 Division Rule am an = am-n Power Rule (am)n = amn Negative Index Rule Unit Fraction Rule Evaluate the following: Write in index form: Consider the following: So in general: 9 8 32 4

  3. Fractional Indices Multiplication Rule am x an = am+n a0 = 1 Division Rule am an = am-n Power Rule (am)n = amn Negative Index Rule Unit Fraction Rule General Fraction Rule Evaluate the following:

  4. Equations Involving Indices Multiplication Rule am x an = am+n a0 = 1 Division Rule am an = am-n Power Rule (am)n = amn Negative Index Rule Unit Fraction Rule General Fraction Rule Solve the following: 62x = 36 •  3x-1 = 9 •  3x-1 = 32 • x - 1 = 2 • x = 3 • (3-1)x = 27 •  3-x = 33 • -x = 3 • x = -3 • 2x-9 = 32 •  2x-9 = 25 • x - 9 = 5 • x = 14 62x = 62 2x = 2  x = 1

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