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.

"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.