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Indices and Roots (F)

Explore indices and roots for GCSE Foundation. Use index laws, square and cube roots, and scientific notation to simplify expressions and calculate efficiently.

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Fascinating Fact:

For file compression, same-base division subtracts powers: 5⁶ ÷ 5² = 5⁴ = 625. Division reduces the exponent.

In GCSE Maths (Foundation), indices and roots help you rewrite numbers neatly and spot patterns. You’ll apply index laws, evaluate powers, and use square and cube roots to solve problems.

Key Terms

Index (exponent): The small power that tells how many times the base is multiplied by itself, e.g., 3⁴.
Base: The number being repeatedly multiplied in a power, e.g., 3 in 3⁴.
Square root: A value which, when multiplied by itself, gives the number, e.g., √81 = 9.

Frequently Asked Questions (Click to see answers)

What are the laws of indices I need for GCSE Foundation?

Key laws: same base multiply adds powers (a^maⁿ = a^m+n); same base divide subtracts powers (a^m⁄aⁿ = a^m−n); power of a power multiplies powers ((a^m)ⁿ = a^mn).

How do I evaluate square and cube roots without a calculator?

Learn perfect squares and cubes: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and 1, 8, 27, 64, 125. Match the number to its root if it’s on the list.

What does a negative or zero index mean?

a⁰ = 1 for a ≠ 0. A negative index means a reciprocal: a⁻ⁿ = 1⁄aⁿ. Apply normal index laws after rewriting.