![]() ![]() Solution: 2x 3 – x 2 + y = 2 (–3) 3 – (–3) 2 + 2 Replace each x with –3, each y with 2. Evaluate 2x 3 – x 2 + y for x = –3, y = 2. Solution: The zero power on the outside means that the value of the entire thing is just 1. If you have a product inside parentheses, and a power on the parentheses, then the power goes on each element inside. This demonstrates the second exponent rule: Whenever you have an exponent expression that is raised to a power, you can multiply the exponent and power: The "to the fourth" means that I'm multiplying four copies of x 2: Solution: Just as with the previous exercise, I can think in terms of what the exponents mean. However, we can NOT simplify (x 4)(y 3), because the bases are different: (x 4)(y 3) = xxxxyyy = (x 4)(y 3). This demonstrates the first basic exponent rule: Whenever you multiply two terms with the same base, you can add the exponents: Using this fact, I can "expand" the two factors, and then work backwards to the simplified form: ![]() "To the third" means "multiplying three copies" and "to the fourth" means "multiplying four copies". To simplify this, I can think in terms of what those exponents mean. The last rule in this lesson tells us that any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power. You can see why this works if you study the example shown.Īccording to the "zero rule," any nonzero number raised to the power of zero equals 1. The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents. Here you see that 5 2 raised to the 3rd power is equal to 5 6. The "power rule" tells us that to raise a power to a power, just multiply the exponents. Adding the exponents is just a short cut! In this example, you can see how it works. The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. This, too, is logical, because one times one times one, as many times as you multiply it, is always equal to one. Secondly, one raised to any power is one. If it's only multiplied one time, then it's logical that it equals itself. This makes sense, because the power shows how many times the base is multiplied by itself. There are two simple "rules of 1" to remember.įirst, any number raised to the power of "one" equals itself. Let's go over each rule in detail, and see some examples. ![]() Exponents are used in many algebra problems, so it's important that we understand the rules for working with exponents. ![]()
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