# 1x 3 write as single power of x

Powers with Variables To generalize the notion of powers fruther, we can imagine any number being multiplied by itself any number of times. Now, here we're going to use the power property of exponents, sometimes called the "power rule. And if you want, you say, hey, Sal, I don't understand why you can add those exponents.

There are many occasions also that one is simply interesting in orders of magnitude, and the exact details of a number are not important. In fact, if we multiply the variable x by itself a number of times say n - times we get: xn. This means that this distance is times a million km note: means 10 mulitiplied by itself 6 times, which is a million. This is just x to the sixth power. We write it in this general notation because it is simpler to state rules this way. So we get x to the sixth power. So let's just use that power property on this expression right over here.

## 6 to the power of 3

Just think of what each property tells you: Negative exponents translate to fractions, and fractional exponents translate to roots and powers. Now imagine trying to use these number in mathematical relationships to calculate some other value; there is a simple clear advantage to the exponential power notation! This means that this distance is times a million km note: means 10 mulitiplied by itself 6 times, which is a million. Take me back to the Main Page Powers: Definition and Simple Powers with Numbers Even though you may not be aware of it, you have already encountered the concept of "raising a number to a power". This notations simply means that if we take the number 3 and multiply it by itself we get 9. Now, here we're going to use the power property of exponents, sometimes called the "power rule. Futhermore, as you will see below, this way of indicating numbers and powers makes the algebraic manipulation of numbers and multiplication of large values much much easier. General rule for negative fractional exponents Practice Problems By Agenturfotografin For each problem below, simplify as much as possible. Here is a summary of what has been mentioned above, in more general notation. Powers - or rather, the exponential notation introduced above - is extremely important in astronomy. This means that three threes multiplied together gives us Now, what does this mean over here? The very basic reason for this is that astronomy forces us to expand our understanding of scales and sizes of objects. Then, we're multiplying that by x squared raised to the fifth power.

Take me back to the Main Page. If 3 is raised to the 2nd power, we get 9 and if 3 is raised to the 3rd power we get And now we have the same base, and we're taking the product, we can just add the exponents. Fractional exponents play a role in computing the orbital period of a planet.

Well, there's a couple of ways to do it.

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