2 To The 3 Power
Exponents Calculator
Estimator Utilize
This is an online calculator for exponents. Calculate the power of large base integers and real numbers. You lot can also calculate numbers to the ability of big exponents less than 2000, negative exponents, and real numbers or decimals for exponents.
For larger exponents endeavour the Large Exponents Calculator
For instructional purposes the solution is expanded when the base ten and exponent northward are small enough to fit on the screen. Generally, this feature is available when base 10 is a positive or negative single digit integer raised to the power of a positive or negative unmarried digit integer. Also, when base ten 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, 3 to the power of 4:
\( 10^n = \; 3^{four} \)
\( = \;3 \cdot 3 \cdot 3 \cdot 3 \)
\( = 81 \)
For example, 3 to the power of -four:
\( x^northward = \;3^{-four} \)
\( = \dfrac{1}{iii^{4}} \)
\( = \; \dfrac{one}{3 \cdot 3 \cdot 3 \cdot iii} \)
\( = \; \dfrac{1}{81} \)
\( = 0.012346 \)
Exponent Note:
Notation that -fourtwo and (-four)two result in different answers: -iv2 = -1 * 4 * four = -sixteen, while (-four)two = (-4) * (-4) = 16. If yous enter a negative value for ten, such equally -4, this estimator assumes (-4)n .
"When a minus sign occurs with exponential notation, a sure caution is in order. For case, (-iv)2 means that -4 is to be raised to the second power. Hence (-four)2 = (-4) * (-4) = 16. On the other hand, -42 represents the additive inverse of ivii. Thus -4ii = -16. Information technology may help to remember of -10ii every bit -1 * x2 ..."[1]
Examples:
- 3 raised to the power of 4 is written 34 = 81.
- -4 raised to the power of 2 is written (-four)2 = sixteen.
- -three raised to the power of 3 is written (-3)3 = -27. Note that in this case the answer is the same for both -three3 and (-iii)iii nevertheless they are withal calculated differently. -three3 = -ane * 3 * 3 * 3 = (-3)three = -3 * -3 * -3 = -27.
- For 0 raised to the 0 ability the answer is i all the same this is considered a definition and non an bodily calculation.
Exponent Rules:
\( 10^chiliad \cdot 10^n = x^{yard+n} \)
\( \dfrac{x^k}{x^n} = x^{m-n} \)
\( (x^yard)^n = x^{thou \cdot n} \)
\( (10 \cdot y)^m = x^chiliad \cdot y^m \)
\( \left(\dfrac{x}{y}\correct)^m = \dfrac{ten^1000}{y^yard} \)
\( x^{-m} = \dfrac{i}{10^thou} \)
\( \left(\dfrac{x}{y}\right)^{-m} = \dfrac{y^k}{x^m} \)
\( x^one = x \)
\( x^0 = 1 \)
\( 0^0 = 1 \; (definition) \)
\( if \; x^chiliad = y \; then \; y = \sqrt[grand]{10} = y^{\frac{1}{m}} \)
\( x^{\frac{chiliad}{north}} = \sqrt[n]{x^m} \)
References
[i] Algebra and Trigonometry: A Functions Approach; M. 50. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Company; 1982, page eleven.
For more detail on Exponent Theory see Exponent Laws.
To summate fractional exponents use our Partial Exponents Reckoner.
To calculate root or radicals use our Roots Calculator.
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2 To The 3 Power,
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