Powers, Roots & Standard Form

These flashcards cover key vocabulary terms and definitions related to Powers, Roots, and Standard Form relevant for the IGCSE International Maths exam.

Powers (or indices)

Small 'floating' numbers that indicate how many times to multiply a base by itself.

Base

The big number at the bottom in powers and roots.

Index (or exponent)

The small number that indicates the power to which the base is raised.

Square root

A number that, when multiplied by itself, gives the original number. For example, √25 = ±5.

Cube root

The number that, when raised to the power of three (cubed), gives the original number. For example, ³√125 = 5.

Nth root

A value that, when raised to the power of n, equals the original number. For example, the 5th root of 243 is 3.

Reciprocal

The number that when multiplied by a given number results in 1. It can also be represented as an index of -1.

Law of Indices

Rules governing operations with powers, applicable to both numbers and algebra.

a^0

Any non-zero number raised to the power of 0 equals 1.

a^1

Any number raised to the power of 1 equals itself.

a^m × a^n

To multiply indices with the same base, add their powers (a^(m+n)).

a^m ÷ a^n

To divide indices with the same base, subtract their powers (a^(m-n)).

a^(-n)

A negative power is the reciprocal: a^(-n) = 1/(a^n).

Standard Form

A way of writing numbers using powers of 10 for simplicity, typically written as a × 10^n.

Converting to Standard Form

Transforming numbers into a × 10^n format, where 1 ≤ a < 10.

Operations with Standard Form

Performing calculations with numbers in standard form, keeping track of the powers of 10.

Estimating Roots

Finding the closest integer roots to approximate a root.