Lesson 7, Topic 1
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# Laws of Indices

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### 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. $$( \frac{a}{b})^{^{-\frac{m}{n}}} = (\frac{b}{a})^{^{\frac{m}{n}}}$$

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