^ | = | ||
use e as base | |||
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What is one exponent?
Exponentiation is a math operation, created as an, involving the base a and also an exponent n. In the instance where n is a optimistic integer, exponentiation synchronizes to repeated multiplication of the base, n times.
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an = a × a × ... × a n times
The chrischona2015.org over accepts an adverse bases, but does no compute imaginary numbers. It also does no accept fractions, however can be provided to compute spring exponents, as lengthy as the exponents are input in their decimal form.
Basic exponent laws and also rules
When exponents the share the same base room multiplied, the exponents are added.
an × am = a(n+m)EX:22 × 24 = 4 × 16 = 64 22 × 24 = 2(2 + 4) = 26 = 64
When an exponent is negative, the an adverse sign is gotten rid of by reciprocating the base and raising it come the confident exponent.
a(-n)= | 1 |
an |
EX: 2(-3) = 1 ÷ 2 ÷ 2 ÷ 2 | = | 1 |
8 |
EX: 2(-3)= | 1 |
23 |
8 |
When exponents the share the same base room divided, the exponents are subtracted.
am |
an |
EX: | 22 |
24 |
16 |
4 |
22 |
24 |
22 |
4 |
When index number are elevated to an additional exponent, the exponents room multiplied.
(am)n = a(m × n)EX: (22)4 = 44 = 256(22)4 = 2(2 × 4) = 28 = 256
When multiply bases are increased to an exponent, the exponent is dispersed to both bases.
(a × b)n = an × bnEX: (2 × 4)2 = 82 = 64(2 × 4)2 = 22 × 42 = 4 × 16 = 64
Similarly, when divided bases are increased to an exponent, the exponent is spread to both bases.
( | a |
b |
bn |
EX: ( | 2 |
5 |
5 |
5 |
25 |
( | 2 |
5 |
52 |
25 |
When one exponent is 1, the base stays the same.
a1 = a
When an exponent is 0, the an outcome of the indexes of any type of base will always be 1, return somedebate surrounds 00 being 1 or undefined. For plenty of applications, defining 00 as 1 is convenient.
a0 = 1
Shown listed below is an example of an debate for a0=1 using among the aforementioned exponent laws.
If an × am = a(n+m)Thenan × a0 = a(n+0) = an
Thus, the only means for an to remain unchanged by multiplication, and also this exponent regulation to remain true, is for a0 to be 1.
When one exponent is a fraction where the numerator is 1, the nth source of the base is taken. Shown listed below is an instance with a fractional exponent wherein the numerator is no 1. It provides both the ascendancy displayed, and also the ascendancy for multiplying index number with like bases disputed above. Keep in mind that the chrischona2015.org can calculate spring exponents, however they have to be entered into the chrischona2015.org in decimal form.
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It is also feasible to compute exponents with negative bases. Castle follow lot the same rules as exponents with optimistic bases. Exponents with an unfavorable bases elevated to confident integers are equal come their hopeful counterparts in magnitude, yet vary based on sign. If the exponent is one even, confident integer, the worths will be same regardless that a optimistic or an unfavorable base. If the exponent is one odd, positive integer, the result will again have the very same magnitude, however will it is in negative. When the rules for fractional exponents with negative bases room the same, castle involve the usage of imaginary numbers due to the fact that it is not possible to take any root that a an unfavorable number. An example is noted below for reference, however please keep in mind that the chrischona2015.org listed cannot compute imagine numbers, and any input that an outcome in an imagine number will return the result "NAN," signifying "not a number." The numerical equipment is basically the very same as the instance with a positive base, other than that the number have to be denoted as imaginary.