1. Properties of Exponents
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To write general rules for properties of exponents, we first need to check that they work, and then find a convenient way to express them.
See solution.
As we can see, multiplying the two same base powers is equivalent to multiplying the base times itself as many times as the sum of the exponents. This will work for all cases, since we have not made any assumption for the values of x, n, or m. Now that we have our general result, we can summarize it and write it as a formula.
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Product of Two Same Base Powers |
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To multiply the two same base powers, simply add their exponents. x^n* x^m = x^(n+m) |
We could do the same for the rest of the cases we worked with in Exploration 1, writing our conclusions as general rules.
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Quotient of Two Same Base Powers |
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To find the quotient of the two same base powers, simply subtract the exponent of the denominator from that in the numerator. x^m/x^n = x^(m-n) |
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Power of a Power |
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To find the result of raising a power to a power, simply multiply the exponents. (x^n)^m = x^(n* m) |
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Power of a Product |
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When a product is raised to a power, the result is the product of the factors raised to that power. ( xy )^n = x^n y^n |
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Power of a Quotient |
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When a quotient is raised to a power, the result is the quotient of the numbers raised to that power. ( x/y )^n = x^n/y^n |