Powers, Roots, and Standard Form Made Easy
Introduction
Powers, roots, and standard form are essential for handling large and small numbers in GCSE Maths. These skills are vital for algebra, geometry, and problem-solving in real-life contexts.
In this article, we’ll explore:
- Understanding powers and indices.
- Calculating square and cube roots.
- Using standard form for large and small numbers.
Powers and Indices
Powers (or indices) represent repeated multiplication.
Basic Rules of Indices
- \( a^m \times a^n = a^{m+n} \)
- \( \frac{a^m}{a^n} = a^{m-n} \)
- \( (a^m)^n = a^{m \times n} \)
Example: Simplify \( 2^3 \times 2^4 \).
- Add powers: \( 2^{3+4} = 2^7 = 128 \).
Square and Cube Roots
A square root reverses squaring a number:
\[
\sqrt{16} = 4 \quad \text{because } 4^2 = 16.
\]Example: Find \( \sqrt{49} \): \( 7 \).
Standard Form
Standard form expresses numbers as:
\[
a \times 10^n \quad (1 \leq a < 10)
\]Converting to Standard Form
- Large numbers: \( 4500 = 4.5 \times 10^3 \).
- Small numbers: \( 0.006 = 6 \times 10^{-3} \).
Practice Question
Question: Write 0.00042 in standard form.
Solution: \( 4.2 \times 10^{-4} \).
Conclusion
Mastering powers, roots, and standard form simplifies calculations and boosts your confidence in GCSE Maths. Practice regularly to tackle exam questions efficiently.
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