This all-in-one online Exponent Calculator is designed to find the exponent x of a number (base) b, where the result r, the base, and the exponent are real numbers. You can enter the values of any two parameters in the input fields of this calculator and find the missing parameter. The letter e can be used for scientific notation or instead of the Euler’s number.
r = bx
What is an Exponent in Math?
Exponentiation is a mathematical operation that involves multiplying a number by itself a certain number of times, denoted by a power or exponent. When we write xn, x is referred to as the base, and n is the exponent or power. In other words, the expression xn represents the product of x multiplied by itself n times:
Exponents may also have negative, fractional, or decimal values. When the exponent is negative, x-n is equivalent to 1 divided by xn . This identity holds for any non-zero number x and any integer n:
In case the exponent is a rational number of the form m/n, where m and n are integers, we define xm/n to be the principal n-th root of a positive real number x raised to the m-th power:
The principal n-th root of x is denoted as x1/n. This means that (x1/n)n = x.
Exponentiation with real numbers can be defined by extending the notion of rational exponents to reals using continuity. Alternatively, we can define exponentiation in terms of powers via logarithms. The result is always a positive real number. The properties and identities that hold for integer exponents are also valid for positive real bases with non-integer exponents.
Exponents Laws and Rules
Multiplying exponents: xm · xn = xm+n, xn · yn = (x · y)n.
Dividing exponents: xm / xn = xm-n, xn / yn = (x / y)n.
Power of exponent: (xm)n = xm+n, xm/n = n√(xm).
Negative exponent: x-n = 1 / xn.
Zero exponent: x0 = 1.
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Check out our other math calculators such as Fraction Exponent Calculator or Rounding Calculator.