Table of Contents
Surds and Indices
Surds and Indices Formulas
Surds
Definition
\[ \sqrt[n]{a} \quad \text{is a surd if } a \text{ is not a perfect nth power.} \]Multiplication of Surds
\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \]Division of Surds
\[ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \]Addition and Subtraction of Like Surds
\[ a\sqrt{b} + c\sqrt{b} = (a + c)\sqrt{b} \] \[ a\sqrt{b} - c\sqrt{b} = (a - c)\sqrt{b} \]Indices
Product of Powers Rule
\[ a^m \times a^n = a^{m+n} \]Quotient of Powers Rule
\[ \frac{a^m}{a^n} = a^{m-n} \]Power of a Power Rule
\[ (a^m)^n = a^{mn} \]Power of a Product Rule
\[ (ab)^n = a^n \times b^n \]Power of a Quotient Rule
\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \]Zero Exponent Rule
\[ a^0 = 1 \quad \text{(where } a \neq 0\text{)} \]Negative Exponent Rule
\[ a^{-n} = \frac{1}{a^n} \]Fractional Exponent Rule
\[ a^{\frac{m}{n}} = \sqrt[n]{a^m} \]MCQ Section
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