Calculator Soup^{®}

**Example entries -4 ^{2} or (-4)^{2} will result in different answers.**

Note that -4^{2} = -1 * 4 * 4 = -16 while (-4)^{2} = (-4) * (-4) = 16. See notes below.

This is an online calculator with exponents. It will handle powers of large integers and decimals. You can also use large exponents, negative exponents, and decimal exponents.

"When a minus sign occurs with exponential notation, a certain caution is in order. For example, (-4)^{2} means that -4 is to be raised to the second power. Hence (-4)^{2} = (-4) * (-4) = 16. On the other hand, -4^{2} represents the additive inverse of 4^{2}. Thus -4^{2} = -16. It may help to think of -x^{2} as -1 * x^{2} ..."[1]

- 3 raised to the power of 4 is written as 3
^{4}= 81. - -4 raised to the power of 2 is written (-4)
^{2}= 16. - -3 raised to the power of 3 is written (-3)
^{3}= -27. Note that in this case -3^{3}= -1 * 3 * 3 * 3 = (-3)^{3}= -3 * -3 * -3 = -27. - For 0 raised to the 0 power the answer is 1 however this is considered a definition and not an actual calculation.

(Each Law for Exponents)

x^{m} * x^{n} = x^{m+n}

x^{m} / x^{n} = x^{m-n}

(x^{m})^{n} = x^{m*n}

(x * y)^{m} = x^{m} * y^{m}

(x / y)^{m} = x^{m} / y^{m}

x^{-m} = 1 / x^{m}

(x / y)^{-m} = y^{m} / x^{m}

x^{1} = x

x^{0} = 1

0^{0} = 1 (definition)

If x^{m} = y then y = ^{m}√y = y^{(1/m)}

x^{m/n} = ^{n}√x^{m}

[1] Algebra and Trigonometry: A Functions Approach; M. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Company; 1982, page 11.

http://mathforum.org/library/drmath/view/55709.html

For more detail on Exponent Theory see http://mathworld.wolfram.com/ExponentLaws.html

To calculate fractional exponents use our Fractional Exponents Calculator.

To calculate root or radicals use our Roots Calculator.

**Cite this content, page or calculator as:**

Furey, Edward "Exponents Calculator" From *http://www.CalculatorSoup.com* - Online Calculator Resource.