7 To The 4th Power
Exponents Figurer
Reckoner Use
This is an online calculator for exponents. Calculate the power of large base integers and real numbers. You can also calculate numbers to the ability of large exponents less than 2000, negative exponents, and existent numbers or decimals for exponents.
For larger exponents try the Large Exponents Calculator
For instructional purposes the solution is expanded when the base 10 and exponent due north are small enough to fit on the screen. By and large, this feature is available when base x is a positive or negative unmarried digit integer raised to the ability 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 single digit integer less than 7 and greater than -7.
For example, 3 to the power of 4:
\( 10^due north = \; iii^{4} \)
\( = \;iii \cdot 3 \cdot 3 \cdot three \)
\( = 81 \)
For example, 3 to the ability of -iv:
\( ten^due north = \;3^{-four} \)
\( = \dfrac{i}{three^{4}} \)
\( = \; \dfrac{ane}{iii \cdot three \cdot iii \cdot iii} \)
\( = \; \dfrac{1}{81} \)
\( = 0.012346 \)
Exponent Notation:
Note that -42 and (-4)ii upshot in different answers: -42 = -i * iv * iv = -16, while (-iv)2 = (-four) * (-4) = 16. If y'all enter a negative value for x, such every bit -iv, this calculator assumes (-4)n .
"When a minus sign occurs with exponential notation, a certain caution is in order. For instance, (-iv)ii means that -4 is to be raised to the second power. Hence (-4)2 = (-iv) * (-4) = 16. On the other hand, -iv2 represents the condiment inverse of 4two. Thus -ivii = -16. It may help to call back of -x2 as -1 * x2 ..."[1]
Examples:
- iii raised to the power of iv is written 34 = 81.
- -4 raised to the power of ii is written (-4)ii = sixteen.
- -3 raised to the power of iii is written (-3)3 = -27. Note that in this example the reply is the same for both -3iii and (-iii)three nonetheless they are yet calculated differently. -three3 = -1 * three * 3 * iii = (-3)iii = -3 * -three * -3 = -27.
- For 0 raised to the 0 power the respond is 1 however this is considered a definition and non an actual calculation.
Exponent Rules:
\( x^k \cdot x^n = x^{m+due north} \)
\( \dfrac{x^thou}{ten^due north} = x^{m-due north} \)
\( (10^m)^n = x^{m \cdot northward} \)
\( (x \cdot y)^yard = 10^m \cdot y^one thousand \)
\( \left(\dfrac{x}{y}\right)^1000 = \dfrac{x^thousand}{y^m} \)
\( x^{-thou} = \dfrac{i}{10^1000} \)
\( \left(\dfrac{x}{y}\right)^{-g} = \dfrac{y^m}{x^thousand} \)
\( x^1 = 10 \)
\( x^0 = 1 \)
\( 0^0 = i \; (definition) \)
\( if \; ten^thousand = y \; then \; y = \sqrt[m]{x} = y^{\frac{1}{m}} \)
\( ten^{\frac{m}{n}} = \sqrt[due north]{10^g} \)
References
[1] Algebra and Trigonometry: A Functions Approach; Thou. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Visitor; 1982, folio 11.
For more than detail on Exponent Theory run across Exponent Laws.
To calculate fractional exponents utilize our Partial Exponents Calculator.
To calculate root or radicals use our Roots Calculator.
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7 To The 4th Power,
Source: https://www.calculatorsoup.com/calculators/algebra/exponent.php
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