In today’s lesson, we will revise multiples of ten; ” powers of ten”. previously, we said that prefixes are basically multiples of ten. and before we learn how to use them, we must revise multiples pf ten. Ten to the power of one is ten. Ten to the power of two is ten multiplied by ten, and is equal to 100. Ten to the power three is 10 by 10 by 10, which is equal to 1000. ten to the power negative one is equal to 1 divided by 10, or one tenth. ten to the power negative 2 is equal to ten to the power 2, which is one hundredth. Ten to the power negative 3 is equal to 1 divided by 10 to the power 3, which is one thousandth. ten to the power zero is equal to one. let us revise multiplication. ten to the power n multiplied by ten to the power m… is equal to ten to the power n plus m. let us solve an example. 10 to the power 2 multiplied by 10 to the power 3 gives us ten to the power 2+3 which is 10 to the power 5 10 to the power negative 2 multiplied by 10 to the power 3 gives us 10 to the power -2+3, which is 10. 10 to the power -2 multiplied by 10 to the power -3 gives us 10 to the power -2 + -3 which is 10 to the power -5 10 to the power -2 multiplied by 10 to the power 2 gives us 10 to the power -2 + 2 which is 10 to the power zero and that is 1. As for division, wee have the relation, 10 to the power n divided by 10 to the power m We raise 10 to the power m from the denominator to the numerator. and the relation becomes 10 to the power n multiplied by 10 to the power -m. and it is equal to 10 to the power n-m. Our first example. 10 to the power 2 divided by 10 to the power 3 We raise 10 to the power 3 from the the denominator to the numerator. and it becomes 10 to the power 2 multiplied by 10 to the power -3, which is equal to 10 to the power 2 – 3, which is 10 to the power -1. Lets take another example. 10 to the power -2 divided by 10 to the power 3. As we already said, we raise 10 to the power 3 from the denominator to the numerator. and it becomes 10 to the power -2 multiplied by 10 to the power -3. And it is equal to 10 to the power -2 – 3, which is 10 to the power -5. our last example is 10 to the power -2 divided by 10 to the power -3, which is equal to 10 to the power -2 multiplied by 10 to the power +3, which is equal to 10 to the power -2 + 3, and it is equal to 10 to the power 1.

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