Below, we give details for each one. To see this rule, we just expand out what the exponents mean. Let's start out with a couple simple examples. The general case works the same way. We just need to keep track of the number of factors we have. This expression can be written in a shorter way using something called exponents.
The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor. If two powers have the same base then we can multiply the powers.
When we multiply two powers we add their exponents. If two powers have the same base then we can divide the powers. Power Rule. The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 5 2 raised to the 3rd power is equal to 5 6.
Quotient Rule. The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents. You can see why this works if you study the example shown. According to the "zero rule," any nonzero number raised to the power of zero equals 1.
Negative Exponents. 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. Rules of 1 There are two simple "rules of 1" to remember. Product Rule The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
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