# Multiplying and dividing indices with different bases in dating

### Multiplication of Values with the Same Base Simplify algebraic equations by multiplying and dividing variables with exponents . In this case we see that y is the base for each exponent expression being we multiply two exponential expressions that have the same base. Today we're going to use the base ten place-value system to derive negative exponents. Don't worry, math is inherently balanced, so the other half of the decimal If we multiply the products together and perform the addition, we arrive Is there a relationship between positive and negative exponents?.

Well, when you're dividing, you subtract exponents if you have the same base. So, this is going to be equal to 12 to the negative seven minus negative five power. You're subtracting the bottom exponent and so, this is going to be equal to 12 to the, subtracting a negative is the same thing as adding the positive, twelve to the negative two power.

And once again, we just have to think about, why does this actually make sense? Well, you could actually rewrite this. If we take the reciprocal of this right over here, you would make exponent positive and then you would get exactly what we were doing in those previous examples with products. And so, let's just do one more with variables for good measure.

### The History of Exponents | Sciencing

Let's say I have X to the negative twentieth power divided by X to the fifth power. Well once again, we have the same base and we're taking a quotient. So, this is going to be X to the negative 20 minus five cause we have this one right over here in the denominator.

So, this is going to be equal to X to the negative twenty-fifth power. And once again, you could view our original expression as X to the negative twentieth and having an X to the fifth in the denominator dividing by X to the fifth is the same thing as multiplying by X to the negative five. In sexagesimal system of math, which is what the Babylonians used, the number would be written 2, Squaring it would produce in modern days, the number number 21, In Babylonia is was written 6,0,9.

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• Multiplying & dividing powers (integer exponents)

This is what the equation, as discovered on another ancient tablet, looked like. Try putting that into your calculator. What if, say, in a complex mathematical formula, you need to calculate something really important. It could be anything and it required knowing what 9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9x9 equaled. And there were a lot of such large numbers in the equation. You can figure out what that number is if you care to. In other words it is shorthand, much as many other symbols in math are shorthand, denoting other meanings and allowing complex formulas to be written in a more concise and comprehensible way. One caveat to keep in mind. Math Home Search Dr. Math Exponents in the Real World Date: Exponents How come we have to know how to add, subtract, multiply, and divide exponents? In the real world when do you use exponents? When do you add them?

### Multiplying & dividing powers (integer exponents) (video) | Khan Academy

When do you subtract them? What about multiplying exponents? When do you divide exponents? Do teachers just teach us them because they can?

## Laws of Exponents

In fact, until about years ago, nobody used exponents, and they were perfectly able to do mathematics. But then some people decided that it got boring always writing out all those "times" symbols, and they decided to use exponents to mean how many times you wrote down the number. I hope you know that when a number is written with an exponent, the whole shebang is called an exponentIAL.