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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

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The basic rule in adding and subtracting variables with exponents is they must be like terms. Like terms consist of the same variable or set of variables raised to the same power. The numerical coefficients of these terms may vary, and these are the elements that undergo the addition or subtraction process. The algebraic expressions 2x, 7x and x are like terms, as well as, 4ab^2 and 21ab^2.

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Because a negative exponent turns the base into its reciprocal, a simple method for dividing negative exponents is letting the negative cancel and multiplying by the positive exponential expression. Regents Prep notes that when multiple exponents have the same base, the terms can be easily divided or multiplied because the exponents themselves can be added or subtracted.

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Exponential function rules are the mathematical guidelines for functions that take the form of f(x) = b^x, where the base is a positive real number. With these functions, the growth rate is proportional to their value.