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Number Base System I | Week 16 Topics2 Quizzes
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Number Base System II | Week 23 Topics
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Number Base System III | Week 32 Topics1 Quiz
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Modular Arithmetic I | Week 42 Topics
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Modular Arithmetic II | Week 53 Topics
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Modular Arithmetic III | Week 64 Topics1 Quiz
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Indices I | Week 73 Topics1 Quiz
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Indices II | Week 81 Topic1 Quiz
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Logarithms I | Week 93 Topics
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Logarithms II | Week 104 Topics1 Quiz
Topic Content:
- Definition of Indices
- Laws of Indices
- Fractions with Negative Index
Definition of Indices:
Indices or index (singular) deals with numbers raised to some power
e.g. a5 is read as “a raised to the power 5”. Here 5 is called the index, power, or quotient while a is called the base.
Indices can also be referred to as exponents.
Laws of Indices:
1. \( \scriptsize X^a \times X^b = X^{a + b} \)
2. \( \scriptsize X^a \div X^b \: or \: \normalsize \frac{X^a}{X^b} \scriptsize = X^{a – b} \)
3. \( \scriptsize X^0 = 1 \)
4. \( \scriptsize X^{-a} = \normalsize \frac {1}{X^a} \)
5. \( \scriptsize \left ( X^a \right)^b = X^{ab}\)
6. \( \scriptsize X^{^{\normalsize \frac{a}{b}}} = (\sqrt [b] {X})^a \)
7. \( \scriptsize X^{^{\normalsize\frac{1}{a}}} = \sqrt [a] {X} \)
Fractions with Negative Index:
When a fraction is raised to a negative index, invert the fraction and then change the negative index into a positive index.
1. \( \left( \frac{a}{b} \right)^{^{-\frac{m}{n}}} = \left(\frac{b}{a}\right)^{^{\frac{m}{n}}} \)
Easy to understand, as per usual.