It is also possible to compute exponents with negative bases. Note that the calculator can calculate fractional exponents, but they must be entered into the calculator in decimal form. It uses both the rule displayed, as well as the rule for multiplying exponents with like bases discussed above. Shown below is an example with a fractional exponent where the numerator is not 1. When an exponent is a fraction where the numerator is 1, the n th root of the base is taken. Thus, the only way for a n to remain unchanged by multiplication, and this exponent law to remain true, is for a 0 to be 1. Shown below is an example of an argument for a 0=1 using one of the previously mentioned exponent laws. For many applications, defining 0 0 as 1 is convenient. When an exponent is 0, the result of the exponentiation of any base will always be 1, although someĭebate surrounds 0 0 being 1 or undefined. When an exponent is 1, the base remains the same. Similarly, when divided bases are raised to an exponent, the exponent is distributed to both bases.

When multiplied bases are raised to an exponent, the exponent is distributed to both bases. When exponents are raised to another exponent, the exponents are multiplied. When exponents that share the same base are divided, the exponents are subtracted. When an exponent is negative, the negative sign is removed by reciprocating the base and raising it to the positive exponent. When exponents that share the same base are multiplied, the exponents are added. It also does not accept fractions, but can be used to compute fractional exponents, as long as the exponents are input in their decimal form. The calculator above accepts negative bases, but does not compute imaginary numbers. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times. Related Scientific Calculator | Log Calculator | Root CalculatorĮxponentiation is a mathematical operation, written as a n, involving the base a and an exponent n.

Define negative exponent rule