4 To The 4th Power
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This is an online calculator for exponents. Calculate the power of large base integers and real numbers. You tin likewise summate numbers to the power of large exponents less than 2000, negative exponents, and existent numbers or decimals for exponents.
For larger exponents attempt the Large Exponents Figurer
For instructional purposes the solution is expanded when the base x and exponent n are pocket-sized enough to fit on the screen. Generally, this feature is available when base ten is a positive or negative single digit integer raised to the ability of a positive or negative single digit integer. Likewise, when base 10 is a positive or negative 2 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:
\( x^due north = \; 3^{4} \)
\( = \;3 \cdot 3 \cdot three \cdot three \)
\( = 81 \)
For instance, 3 to the power of -four:
\( 10^due north = \;3^{-4} \)
\( = \dfrac{1}{three^{4}} \)
\( = \; \dfrac{1}{3 \cdot 3 \cdot 3 \cdot iii} \)
\( = \; \dfrac{one}{81} \)
\( = 0.012346 \)
Exponent Notation:
Note that -four2 and (-4)2 result in dissimilar answers: -42 = -1 * 4 * 4 = -16, while (-four)ii = (-4) * (-four) = 16. If yous enter a negative value for x, such equally -4, this estimator assumes (-four)northward .
"When a minus sign occurs with exponential note, a certain caution is in lodge. For instance, (-4)2 means that -4 is to be raised to the second power. Hence (-4)ii = (-iv) * (-4) = 16. On the other manus, -iv2 represents the condiment inverse of 42. Thus -42 = -xvi. Information technology may aid to think of -ten2 as -1 * x2 ..."[ane]
Examples:
- 3 raised to the ability of 4 is written 34 = 81.
- -4 raised to the ability of ii is written (-iv)2 = sixteen.
- -3 raised to the ability of 3 is written (-iii)3 = -27. Note that in this case the reply is the same for both -33 and (-3)three yet they are still calculated differently. -threeiii = -ane * three * iii * 3 = (-3)three = -3 * -iii * -3 = -27.
- For 0 raised to the 0 power the answer is i still this is considered a definition and non an actual calculation.
Exponent Rules:
\( x^m \cdot x^northward = ten^{1000+n} \)
\( \dfrac{x^g}{x^n} = x^{k-n} \)
\( (x^m)^northward = 10^{m \cdot due north} \)
\( (x \cdot y)^m = x^thousand \cdot y^m \)
\( \left(\dfrac{ten}{y}\correct)^m = \dfrac{x^m}{y^1000} \)
\( ten^{-chiliad} = \dfrac{one}{ten^m} \)
\( \left(\dfrac{x}{y}\right)^{-g} = \dfrac{y^m}{x^m} \)
\( x^1 = x \)
\( ten^0 = 1 \)
\( 0^0 = 1 \; (definition) \)
\( if \; x^thou = y \; then \; y = \sqrt[m]{x} = y^{\frac{1}{yard}} \)
\( x^{\frac{m}{n}} = \sqrt[n]{ten^m} \)
References
[1] Algebra and Trigonometry: A Functions Arroyo; M. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Visitor; 1982, folio eleven.
For more than detail on Exponent Theory see Exponent Laws.
To calculate fractional exponents apply our Partial Exponents Computer.
To calculate root or radicals use our Roots Calculator.
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4 To The 4th Power,
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