1 is the nothingness of multiplication. Multiplying and dividing by 1 does nothing to a number. Just like how adding or subtracting zero does nothing. So when we are using powers, we start with 1 then multiply it by the base the necessary number of times. 7^3 =1*7*7*7 7^2=1*7*7 7^1=1*7 7^0=1 7^-1=1/7 7^-2=1/7/7 7^-3=1/7/7/7
Anyone see a problem here? At :54 on the timeline you state "multiply it together five times. You multiplied it together only four times. 1 time 2x2 2 times 2x2x2 3 times 2x2x2x2 4 times 2x2x2x2x2 5 times 2x2x2x2x2x2 Saying one thing and show another thing is very confusing. I have always struggled to comprehend exponents but this continues the confusion.
A better way to understand it when encountering 2^3 or any, is not "multiplying(×) 3 times" like this 2(×)2(×)2(×)2 instead put the base number and 'use' it 3 times for multiplication ex: 2(x)2(x)2 Note: Noticed that there are only 3 whole numbers instead of 4?
You explanation does not explain concept! A much better way to teach the concept of exponents is to use factors. Multiplication is combining factors. When factors are the same instead of writing them all out we use an exponent to say how many factors of the base we have. So 2^5 means 5 factors of 2. This is 2x2x2x2x2. I am truly surprised at how many people have not understood this. It does away with the confusion of whether 2^3 is 8 or 16. 2 multiplied by itself 3 times. Does one start with 2 and then multiply it by itself 3 times to give 16? Or does one include the initial 2 and get 8. I have taught Maths for 45 years and once students understand that the exponent is the number of factors they understand the basic exponential rules. They know why not just how. How would you e xplain 2^4 x 2^3? I would say how many factors of 2 are there? 4 and 3 so that means 7 factors of 2. 2^7. I would like to read other comments on this.
