In this topic you will learn how to work with powers (indices) and how to write very large or very small numbers using standard form. We cover the rules for positive, zero, negative and fractional indices, and how to simplify expressions quickly.
What is an index?The index (or power/exponent) tells us how many times to multiply the base by itself.Example: 53 = …
View LessonZero IndexAny non-zero number to the power 0 equals 1.a0 = 1 (where a ≠ 0)Example: 70 = 1, (3x)0 …
View LessonFractional Indicesa1/n = n√a (the nth root of a)am/n = (n√a)m = n√amExamples91/2 = √9 = 381/3 = 3√8 = …
View LessonWhat is Standard Form?A way of writing very large or very small numbers as a × 10n where 1 ≤ …
View LessonSimplify fully:x4 × x3a9 ÷ a2(m2)5p6 × p × p2(23)2
View Exercise Submit ExerciseWrite with positive indices only:x-35-21/y-52a-1(3x)-2
View Exercise Submit ExerciseWrite in standard form:780000.0005642.10.097391000000
View Exercise Submit ExerciseSimplify, leaving answers with positive indices:x1/2 × x1/2(y1/3)6a2/3 ÷ a1/3(8x3y6)1/3
View Exercise Submit ExerciseCalculate, giving answers in standard form:(3 × 105) × (2 × 103)(6 × 107) ÷ (3 × 104)(4 × 10-2) …
View Exercise Submit Exercise