11 To The 3rd Power

Exponents Reckoner

Calculator Use

This is an online calculator for exponents. Calculate the power of large base integers and existent numbers. You can as well calculate numbers to the power of large exponents less than 2000, negative exponents, and existent numbers or decimals for exponents.

For larger exponents endeavor the Large Exponents Calculator

For instructional purposes the solution is expanded when the base x and exponent n are small enough to fit on the screen. Generally, this feature is bachelor when base x is a positive or negative single digit integer raised to the power of a positive or negative single digit integer. Also, when base x is a positive or negative two digit integer raised to the power of a positive or negative single digit integer less than seven and greater than -7.

For example, 3 to the power of 4:

\( x^northward = \; three^{4} \)

\( = \;iii \cdot iii \cdot three \cdot three \)

\( = 81 \)

For instance, 3 to the ability of -iv:

\( x^due north = \;3^{-4} \)

\( = \dfrac{1}{three^{4}} \)

\( = \; \dfrac{1}{iii \cdot iii \cdot 3 \cdot three} \)

\( = \; \dfrac{i}{81} \)

\( = 0.012346 \)

Exponent Notation:

Note that -iv² and (-4)² result in different answers: -4² = -1 * 4 * 4 = -16, while (-4)² = (-4) * (-4) = 16. If you enter a negative value for ten, such as -4, this calculator assumes (-4)ⁿ .

"When a minus sign occurs with exponential notation, a certain circumspection is in order. For case, (-four)² means that -four is to be raised to the second ability. Hence (-4)² = (-4) * (-4) = 16. On the other hand, -4² represents the additive inverse of 4ⁱⁱ. Thus -4² = -16. It may assist to think of -tenⁱⁱ as -ane * xⁱⁱ ..."[one]

Examples:

iii raised to the power of 4 is written 3^iv = 81.
-four raised to the power of 2 is written (-four)² = 16.
-three raised to the power of 3 is written (-3)ⁱⁱⁱ = -27. Notation that in this case the answer is the aforementioned for both -3³ and (-iii)³ even so they are still calculated differently. -iii³ = -i * 3 * 3 * three = (-3)³ = -3 * -3 * -iii = -27.
For 0 raised to the 0 power the respond is i however this is considered a definition and not an actual calculation.

Exponent Rules:

\( x^k \cdot 10^n = ten^{m+northward} \)

\( \dfrac{x^m}{10^n} = x^{chiliad-due north} \)

\( (x^m)^n = x^{g \cdot n} \)

\( (x \cdot y)^m = ten^thou \cdot y^m \)

\( \left(\dfrac{x}{y}\correct)^m = \dfrac{x^one thousand}{y^m} \)

\( x^{-yard} = \dfrac{ane}{10^m} \)

\( \left(\dfrac{x}{y}\right)^{-m} = \dfrac{y^k}{x^chiliad} \)

\( 10^i = ten \)

\( x^0 = 1 \)

\( 0^0 = 1 \; (definition) \)

\( if \; ten^thou = y \; then \; y = \sqrt[yard]{x} = y^{\frac{i}{m}} \)

\( ten^{\frac{m}{n}} = \sqrt[n]{x^k} \)

References

[1] Algebra and Trigonometry: A Functions Approach; K. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Visitor; 1982, page eleven.

For more than detail on Exponent Theory see Exponent Laws.

To calculate fractional exponents use our Fractional Exponents Calculator.

To summate root or radicals utilise our Roots Calculator.

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