7 To The 6th Power
Exponents Calculator
Computer Use
This is an online computer for exponents. Summate the ability of large base integers and existent numbers. You can too summate numbers to the power of large exponents less than 2000, negative exponents, and real numbers or decimals for exponents.
For larger exponents try the Large Exponents Calculator
For instructional purposes the solution is expanded when the base ten and exponent northward are modest plenty to fit on the screen. Generally, this characteristic is available when base x is a positive or negative single digit integer raised to the power of a positive or negative single digit integer. Too, when base x is a positive or negative 2 digit integer raised to the ability of a positive or negative single digit integer less than 7 and greater than -7.
For example, 3 to the power of 4:
\( ten^northward = \; iii^{4} \)
\( = \;iii \cdot three \cdot iii \cdot iii \)
\( = 81 \)
For example, 3 to the power of -4:
\( 10^n = \;iii^{-iv} \)
\( = \dfrac{1}{3^{4}} \)
\( = \; \dfrac{i}{three \cdot three \cdot three \cdot 3} \)
\( = \; \dfrac{1}{81} \)
\( = 0.012346 \)
Exponent Notation:
Notation that -4two and (-4)2 issue in different answers: -42 = -one * 4 * 4 = -sixteen, while (-4)2 = (-4) * (-4) = 16. If you enter a negative value for ten, such as -4, this calculator assumes (-4)due north .
"When a minus sign occurs with exponential notation, a sure caution is in social club. For instance, (-4)2 means that -four is to exist raised to the 2nd power. Hence (-4)2 = (-4) * (-4) = 16. On the other mitt, -4ii represents the condiment inverse of ivtwo. Thus -42 = -16. It may help to remember of -x2 as -1 * x2 ..."[one]
Examples:
- 3 raised to the power of iv is written threeiv = 81.
- -4 raised to the power of 2 is written (-4)2 = 16.
- -iii raised to the power of 3 is written (-3)3 = -27. Note that in this example the answer is the same for both -33 and (-3)iii even so they are still calculated differently. -33 = -1 * 3 * 3 * 3 = (-iii)3 = -3 * -iii * -3 = -27.
- For 0 raised to the 0 power the answer is 1 all the same this is considered a definition and not an bodily calculation.
Exponent Rules:
\( x^g \cdot x^n = x^{thousand+n} \)
\( \dfrac{x^chiliad}{x^n} = x^{m-n} \)
\( (10^g)^n = x^{m \cdot n} \)
\( (10 \cdot y)^m = x^grand \cdot y^one thousand \)
\( \left(\dfrac{ten}{y}\right)^thousand = \dfrac{ten^1000}{y^m} \)
\( x^{-m} = \dfrac{ane}{x^m} \)
\( \left(\dfrac{x}{y}\right)^{-m} = \dfrac{y^yard}{ten^grand} \)
\( ten^ane = x \)
\( x^0 = 1 \)
\( 0^0 = i \; (definition) \)
\( if \; ten^m = y \; then \; y = \sqrt[m]{x} = y^{\frac{1}{grand}} \)
\( ten^{\frac{thousand}{north}} = \sqrt[n]{x^grand} \)
References
[1] Algebra and Trigonometry: A Functions Arroyo; 1000. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Company; 1982, folio 11.
For more detail on Exponent Theory see Exponent Laws.
To calculate partial exponents employ our Fractional Exponents Calculator.
To calculate root or radicals use our Roots Computer.
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7 To The 6th Power,
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