License Terms: IMathAS Community License CC-BY + GPL The assumptions here are latexb e 0 /latex and latexm /latex and latexn /latex are any integers. License Terms: IMathAS Community License CC-BY + GPL When multiplying exponential expressions with the same base where the base is a nonzero real number, copy the common base then add their exponents. Simplify Expressions With Negative Exponents.License: Public Domain: No Known Copyright License Terms: Download for free at Simplify Expressions With Zero Exponents. So here you just add the exponents and once again you would get X to the negative twenty-fifth power.Use the zero exponent and other rules to simplify each expression. View our original expression as X to the negative twentieth and having an X to theįifth in the denominator dividing by X to the fifth is the same thing as multiplying by X to the negative five. So, this is going to be equal to X to the negative twenty-fifth power. The negative 20 minus five cause we have this one right Well once again, we have the same base and we're taking a quotient. Negative twentieth power divided by X to the fifth power. This rule states that when you have a negative exponent, you can simplify the expression to get the solution by. And so, let's just do one more with variables for good measure. Of this right over here, you would make exponent positive and then you would getĮxactly what we were doing in those previous examples with products. 12 to the negative seven divided by 12 to the negative five, that's the same thing asġ2 to the negative seven times 12 to the fifth power. Have to think about, why does this actually make sense? Well, you could actually rewrite this. You're subtracting the bottom exponent and so, this is going toīe equal to 12 to the, subtracting a negative is the same thing as adding the positive, twelve to the negative two power. So, this is going to be equal to 12 to the negative seven minus negative five power. So, what if I were to ask you, what is 12 to the negative seven divided by 12 to the negative five power? Well, when you're dividing, you subtract exponents if With one over A times A, which is the same thing asĪ to the negative two power. That cancels with that, and you're still left This right over here, that is one over A times A times A times A and then this is times A times A, so that cancels with that, Since I'm multiplying them, you can just add the exponents. Think of it this way: in order to change the exponent in b (-a) from -a to positive a, you move the entire value from the numerator to the denominator to get 1/ (ba). If you have two positive real numbers a and b then b (-a)1/ (ba). What is that going to be? Well once again, you have the same base, in this case it's A, and so This lesson will cover how to find the power of a negative exponent by using the power rule. So let's say that you have A to the negative fourth power times A to the, let's say, A squared. So this four times four is the same thing as four squared. When we combine like terms by adding and subtracting, we need to have the same base with the same exponent. And so you're going to be left with five minus three, or negative three plus five fours. In the expression am with positive integer m and a 0, the exponent m tells us how many times we use the base a as a factor. The exponent p1is always negative, exponents p2and p3are positive and it is. And so, three of these in the denominator are going to cancel out with three of these in the numerator. The rule of replacement of the Kasner exponents remains, of course, the same. And so notice, when you multiply this out, you're going to have fiveįours in the numerator and three fours in the denominator. So it's times four times four times four times four times four. And then four to the fifth, that's five fours being Simplify Simplify Simplify Simplify Simplify. Choose 'Simplify' from the topic selector and click to see the result in our Algebra Calculator Examples. Four to the negative 3 power, that is one over four to the third power, or you could view that as one over four times four times four. The exponent calculator simplifies the given exponential expression using the laws of exponents. And that's just a straightįorward exponent property, but you can also think about why does that actually make sense. Four to the negative three plus five power which is equal to four See look, I'm multiplying two things that have the same base, so this is going to be that base, four. Well there's a couple of ways to do this. And I encourage you to pause the video and think about it on your own. So, let's think about whatįour to the negative three times four to the fifth power is going to be equal to. Let's get some practice with our exponent properties, especially when we have integer exponents.
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