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Exponents Calculator

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Exponent Notation:

Example entries -42 or (-4)2 will result in different answers.
Note that -42 = -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, -42 represents the additive inverse of 42. Thus -42 = -16. It may help to think of -x2 as -1 * x2 ..."[1]

Example:

  • 3 raised to the power of 4 is written as 34 = 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 -33 = -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.

Exponent Laws:
(Each Law for Exponents)

xm * xn = xm+n

xm / xn = xm-n

(xm)n = xm*n

(x * y)m = xm * ym

(x / y)m = xm / ym

x-m = 1 / xm

(x / y)-m = ym / xm

x1 = x

x0 = 1

00 = 1 (definition)

If xm = y then y = m√y = y(1/m)

xm/n = n√xm

References

[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.