10 To The Negative 5
Exponents Calculator
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This is an online figurer for exponents. Calculate the power of large base integers and real numbers. You can besides calculate numbers to the power of big exponents less than 2000, negative exponents, and real numbers or decimals for exponents.
For larger exponents try the Large Exponents Estimator
For instructional purposes the solution is expanded when the base 10 and exponent north are minor plenty to fit on the screen. Generally, this characteristic is bachelor when base 10 is a positive or negative single digit integer raised to the power of a positive or negative unmarried digit integer. Too, when base ten is a positive or negative 2 digit integer raised to the ability of a positive or negative single digit integer less than vii and greater than -7.
For example, iii to the power of iv:
\( ten^n = \; iii^{four} \)
\( = \;3 \cdot 3 \cdot three \cdot 3 \)
\( = 81 \)
For example, 3 to the power of -4:
\( x^northward = \;iii^{-4} \)
\( = \dfrac{1}{iii^{4}} \)
\( = \; \dfrac{1}{iii \cdot iii \cdot 3 \cdot three} \)
\( = \; \dfrac{i}{81} \)
\( = 0.012346 \)
Exponent Notation:
Note that -42 and (-4)2 result in dissimilar answers: -42 = -1 * 4 * four = -16, while (-iv)2 = (-iv) * (-4) = sixteen. If you enter a negative value for x, such every bit -4, this reckoner assumes (-4)northward .
"When a minus sign occurs with exponential notation, a sure caution is in order. For case, (-4)2 means that -4 is to be raised to the second power. Hence (-four)ii = (-four) * (-4) = 16. On the other hand, -42 represents the additive inverse of 42. Thus -4two = -16. Information technology may aid to recall of -xii every bit -1 * x2 ..."[1]
Examples:
- 3 raised to the ability of 4 is written 3iv = 81.
- -4 raised to the power of 2 is written (-iv)2 = xvi.
- -iii raised to the power of iii is written (-three)3 = -27. Annotation that in this instance the answer is the same for both -33 and (-3)3 however they are still calculated differently. -33 = -i * 3 * 3 * 3 = (-3)3 = -3 * -3 * -iii = -27.
- For 0 raised to the 0 power the reply is i nevertheless this is considered a definition and not an bodily calculation.
Exponent Rules:
\( x^grand \cdot x^n = x^{m+northward} \)
\( \dfrac{ten^yard}{10^n} = ten^{m-n} \)
\( (x^grand)^n = ten^{m \cdot n} \)
\( (ten \cdot y)^chiliad = x^m \cdot y^m \)
\( \left(\dfrac{x}{y}\right)^m = \dfrac{x^m}{y^g} \)
\( x^{-m} = \dfrac{1}{x^grand} \)
\( \left(\dfrac{x}{y}\right)^{-m} = \dfrac{y^g}{x^thou} \)
\( x^i = x \)
\( x^0 = ane \)
\( 0^0 = 1 \; (definition) \)
\( if \; x^one thousand = y \; then \; y = \sqrt[m]{x} = y^{\frac{1}{m}} \)
\( 10^{\frac{chiliad}{n}} = \sqrt[n]{x^m} \)
References
[1] Algebra and Trigonometry: A Functions Approach; Yard. L. Keedy and Marvin L. Bittinger; Addison Wesley Publishing Visitor; 1982, page xi.
For more than detail on Exponent Theory see Exponent Laws.
To summate fractional exponents use our Partial Exponents Reckoner.
To summate root or radicals employ our Roots Figurer.
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10 To The Negative 5,
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