Laws of indices
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 7 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Powers everywhere
- Index notation
- Multiplying powers
- Dividing powers
Read the transcript of the teaching part
Last time
Before we start: last time, in Compound interest and exponential growth, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Powers everywhere
One bacterium splits into two, then four, then eight. After ten hours there are two to the power ten, over a thousand. Powers describe fast growth, tiny sizes, and roots. Today you learn the laws that let you simplify any power, including zero, negative and fractional ones.
Index notation
In five to the power four, five is the base and four is the power, also called the index or exponent. It means five multiplied by itself four times. The laws of indices only work when the bases are the same.
Multiplying powers
When you multiply powers of the same base, add the indices. Five to the four, times five cubed: that is four fives, then three more fives, seven fives altogether.
Dividing powers
When you divide powers of the same base, subtract the indices. Seven to the nine, divided by seven to the five, is seven to the four. The numbers in front do not change: they are just numbers. Only the indices of the same base are combined.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Laws of indices.
The whole chapter: Indices, Standard Form and Surds.
Chapter 4: Indices, standard form and surds
- Laws of indices 5 min
- Standard form 5 min
- Surds 5 min
Also for O Level Maths 4024
Which topics come up most in O Level Maths 4024 past papers, counted from every paper since 2004.