Raise To The Third Power

Exponents Calculator

Calculator Use

This is an online calculator for exponents. Summate the power of big base of operations integers and real numbers. You can besides calculate numbers to the power of big exponents less than 2000, negative exponents, and existent numbers or decimals for exponents.

For larger exponents endeavour the Large Exponents Computer

For instructional purposes the solution is expanded when the base 10 and exponent n are small-scale enough to fit on the screen. By and large, this characteristic is available when base x is a positive or negative unmarried digit integer raised to the power of a positive or negative unmarried digit integer. Also, when base x is a positive or negative two digit integer raised to the power of a positive or negative unmarried digit integer less than seven and greater than -7.

For example, three to the power of iv:

\( ten^northward = \; iii^{4} \)

\( = \;3 \cdot 3 \cdot three \cdot 3 \)

\( = 81 \)

For example, iii to the power of -4:

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

\( = \dfrac{1}{3^{iv}} \)

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

\( = \; \dfrac{1}{81} \)

\( = 0.012346 \)

Exponent Annotation:

Notation that -four² and (-4)ⁱⁱ result in unlike answers: -4² = -1 * 4 * 4 = -16, while (-4)² = (-4) * (-4) = sixteen. If yous enter a negative value for x, such every bit -4, this calculator assumes (-iv)ⁿ .

"When a minus sign occurs with exponential notation, a certain circumspection is in guild. For instance, (-4)² means that -4 is to be raised to the second power. Hence (-iv)² = (-4) * (-4) = sixteen. On the other paw, -4² represents the condiment changed of 4ⁱⁱ. Thus -4^two = -16. It may help to think of -x² as -one * x² ..."[1]

Examples:

3 raised to the ability of 4 is written three^four = 81.
-four raised to the ability of two is written (-4)² = 16.
-iii raised to the power of 3 is written (-3)^three = -27. Note that in this case the respond is the same for both -iii³ and (-3)³ still they are still calculated differently. -3ⁱⁱⁱ = -i * 3 * 3 * 3 = (-three)ⁱⁱⁱ = -iii * -three * -3 = -27.
For 0 raised to the 0 ability the reply is ane however this is considered a definition and not an bodily adding.

Exponent Rules:

\( x^yard \cdot 10^north = 10^{g+due north} \)

\( \dfrac{x^chiliad}{ten^north} = ten^{thou-n} \)

\( (x^grand)^northward = x^{thou \cdot n} \)

\( (x \cdot y)^m = x^grand \cdot y^m \)

\( \left(\dfrac{x}{y}\right)^thou = \dfrac{x^m}{y^m} \)

\( x^{-g} = \dfrac{1}{x^chiliad} \)

\( \left(\dfrac{ten}{y}\right)^{-grand} = \dfrac{y^m}{x^one thousand} \)

\( ten^one = x \)

\( 10^0 = 1 \)

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

\( if \; x^k = y \; then \; y = \sqrt[1000]{x} = y^{\frac{1}{chiliad}} \)

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

References

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

For more detail on Exponent Theory encounter Exponent Laws.

To summate fractional exponents use our Fractional Exponents Calculator.

To calculate root or radicals use our Roots Calculator.

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