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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.

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.

## Similar Questions

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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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The quotient of powers property states that when two powers with the same base are divided, the exponents are subtracted from each other. This is written out in the formula: (a^b)/(a^c)=a^b-c.

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If an exponent is a fraction, such as y^1/n, the correct operation is to take the nth root of the base number y. For example, 27^1/3 is the same thing as taking the cube root of 27, so the answer is 3.