Powers and Roots

Summary and Exam Tips for Powers and Roots

Powers and Roots is a subtopic of Numbers and the Number System, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. Powers involve multiplying a number by itself multiple times, expressed as $a^n$. Key rules include: when multiplying indices with equal bases, add the powers ($a^m \times a^n = a^{m+n}$); when dividing, subtract the powers ($a^m \div a^n = a^{m-n}$); a power of a power is found by multiplying the powers ($(a^m)^n = a^{m \times n}$); and negative powers are converted to positive by taking the reciprocal ($a^{-n} = \frac{1}{a^n}$).

Roots are the inverse of powers, represented by the radical symbol $\sqrt{}$. For example, $\sqrt[3]{27} = 3$. Higher order roots use symbols like $\sqrt[3]{}, \sqrt[4]{},$ etc. Calculators can be used to find powers and roots efficiently, such as calculating $4^5 = 1024$ or $\sqrt{9} = 3$.

Exam Tips

• Understand the Rules: Familiarize yourself with the four key rules of powers and roots. Practice applying these rules to different problems.
• Use Calculators Wisely: Know how to use your calculator for powers and roots to save time during exams.
• Practice Problems: Solve a variety of problems involving both powers and roots to build confidence and speed.
• Check Your Work: Always double-check your calculations, especially when dealing with negative powers or higher order roots.
• Visualize Concepts: Draw diagrams or write out steps to better understand the relationships between powers and roots.