![]() ![]() The answer becomes one over the base of x raised to the power of +4. Negative exponent with Quotient Rule:Īlgebraic Problem: Again, subtraction "top" minus "bottom" exponents. Remember, with negative exponents, the answer becomes one over the base with the exponent changed to positive.ġ0. Numerical Problem: The Quotient Rule subtraction is always done "top" minus "bottom" exponents. This example also shows the Power to Power Rule for ( x 3) 2 = x 6, The power of -2 in this problem affects both the -8 and the x 3. Don't forget to "invert" the second term when dividing. Apply the rule for dealing with a negative exponent. Remember that the "FRACTION BAR" means division. Combing the results to form the final answer. If it was to be attached to " a", a parentheses would be used.Įach variable has its own assigned exponent, so they are treated separately. In this problem, the exponent is not attached to the variable " a". Sneaky one!!!! Remember that the exponent belongs only to the base value to which it is attached. The negative 1 exponent indicates that the value is the same as 1 over 3 to a power of positive 1.īe sure to keep the negative base in a set of parentheses to avoid calculation errors.īe careful with values not being affected by the exponent (in this case the 6). ![]() It can be thought of as a form of repeated division by the base:Įxamples: (numerical and algebraic applications) 1. The use of a negative exponent produces the opposite of repeated multiplication. It's correct either way.The use of a positive exponent is an application of repeated multiplication by the base: When you get really good, you'll see that a -1 exponent really just flips the fraction. Of course, we're still inside the parentheses.įinally, the -1 exponent can be multiplied to both of the other exponents as well as the whole number in the numerator. Next, since we need positive exponents, we can use the quotient rule for the x's and y's separately. We can also take care of those pesky coefficients by dividing 10 by 5. We'll work inside out using the product and power rules. To start, we'll take care of the stuff inside the parentheses in both the numerator and denominator. We're sure it's no problem for a well-trained Shmooper like you.Īll we need to do is keep the x's with the x's and the y's with the y's, and deal with the coefficients separately. This is crazy-looking, but it's definitely a good summary of all our rules up to this point. Anyway, here's our work for this problem-o. But remember, anything raised to the 0 is 1. If you went ahead and did all the work for this one before realizing it was all raised to the power of 0, we apologize. In this particular problem, we multiply the -8 and 7 while adding the exponents. This tends to make things just a bit more confusing because we still need to treat the coefficients like normal numbers while applying exponent rules to the exponents. In this problem, the -8 and 7 are coefficients. In case you weren't awake in the first section, coefficients are the numbers in front of or multiplied by the variables. Simplify using positive exponents: (-8 z -6)(7 z 3). Next, we'll multiply 12 by 3 to get 36 before subtracting 4.Īs long as we can add, multiply, and subtract, we're golden.Īnyone ready for the coefficients? Sample Problem First, we're going to take care of what's in the parentheses by adding exponents. ![]() Yikes, we're going right for the jugular here all three rules at once. We need to take the lovely exponent in the numerator and subtract it from the exponent in the denominator. This is important in case we get asked to simplify using only positive exponents. The same thing works in the other direction too-if the bigger exponent is in the denominator. This leaves us with three x's, otherwise known as x 3. Since x divided by x is 1, we can divide out two x's on the top and bottom. That's five x's on top and just two x's below. You might want to think of it this way: Multiplying out the numerator and denominator gives us. This brings us to a new rule: whenever like bases are divided, we subtract the exponent in the denominator from the one in the numerator. Could life be any more awesome right now? Whenever a base is moved to the other side of a fraction bar, the exponent of that base switches from negative to positive. It's the line between the numerator and denominator. No, that's not a bar where the fractions all hang out and have a good time. If you don't know already, the main idea here is that exponents switch signs whenever they're moved to the opposite side of a fraction bar. That's simply because negative exponents have a bit of a mind of their own. ![]() You may or may not have noticed that you've yet to see any negative exponents. ![]()
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