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# What is the product rule for exponents?

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The product rule for exponents state that when two numbers share the same base, they can be combined into one number by keeping the base the same and adding the exponents together. All multiplication functions follow this rule, even simple ones like 2*2, where both 2s have an exponent of one. Using the rule, the result will by 2^2, which is equal to 4.

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There are many rules that simplify mathematical operations that involve exponents. A similar rule to the product rule is the quotient rule, which can be used when one number is being divided by another. As long as the numerator and denominator have the same base number, they can be combined into one number with an exponent that is equal to the exponent of the numerator minus the exponent of the denominator.

A number with an exponent can also be put to an additional exponent. In order to simplify, the power rule can be used. The power rule states that when a number with an exponent is put to another exponent, the exponents can be multiplied together. For example, (2^3)^2 could be simplified as 2^6, since 3*2 equals 6. Both of these forms will result in the same final answer, but simplified versions are easier to work with.

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## Related Questions

• A:

An exponent is a shorthand way of showing how many times to multiply a number by itself. The number 9 with a small raised 3 on its upper right, also commonly expressed as 9^3, represents the base of 9 to the 3rd power, for instance; the raised 3 is the exponent. Simplify multiplication of two exponents with the same base number using exponent addition.

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Euclid discovered the concept underlying the exponent, calling the area of a square a power of the length of a single side. Archimedes later generalized the idea of powers in his work, "The Sand Reckoner." He discovered and proved the law of exponents in the same work.

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The distributive property of exponents is a mathematical rule that applies to an exponent that acts on a term that is within parentheses. It says that if there is a single term in the base, such as "3x," and it is raised to a certain power, like "(3x)^6," the exponent applies to all parts of the term, in this case to both the three and the "x."