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.
Know MoreThere 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.
Learn more about ExponentsThe Greek mathematician Archimedes is credited with discovering and proving the law of exponents in "The Sand Reckoner." His famous work was designed to express the number of grains of sand that can fit in the universe, leading to a discussion about the way to refer to large numbers.
Full Answer >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.
Full Answer >Logarthims of the same base can be added together by multiplying their arguments and then performing the logarithm on the product. For example, assuming log means log base 10 as it does on a calculator: log(x) + log(y) = log(x * y)
Full Answer >When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to the third power. When adding or subtracting different bases with the same power, evaluate the exponents first, and then perform the summation.
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