^=
use e as base
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What is an exponent?

Exponentiation is a mathematical operation, composed as an, entailing the base a and an exponent n. In the case where n is a confident integer, exponentiation corresponds to repeated multiplication the the base, n times.

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an = a × a × ... × a n times

The doyourpartparks.org over accepts an unfavorable bases, yet does no compute imaginary numbers. It likewise does no accept fractions, yet can be provided to compute fractional exponents, as long as the exponents room input in their decimal form.

Basic exponent laws and rules

When exponents the share the same base are multiplied, the exponents space added.

an × am = a(n+m)EX:22 × 24 = 4 × 16 = 64 22 × 24 = 2(2 + 4) = 26 = 64

When one exponent is negative, the negative sign is removed by reciprocating the base and raising it come the hopeful exponent.

a(-n)=1
an
EX: 2(-3) = 1 ÷ 2 ÷ 2 ÷ 2 =1
8
EX: 2(-3)=1
23
=1
8

When exponents that share the very same base space divided, the exponents are subtracted.

am
an
= a(m - n)
EX: 22
24
=4
16
=1
4
22
24
= 2(2-4) = 2-2 =1
22
=1
4

When exponents are increased to one more 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 distributed to both bases.

(a × b)n = one × bnEX: (2 × 4)2 = 82 = 64(2 × 4)2 = 22 × 42 = 4 × 16 = 64

Similarly, when separated bases are increased to one exponent, the exponent is spread to both bases.

(a
b
)n=an
bn
EX: (2
5
)2=2
5
×2
5
=4
25
(2
5
)2=22
52
=4
25

When one exponent is 1, the base continues to be the same.

a1 = a

When one exponent is 0, the result of the indices of any base will constantly be 1, return somedebate surrounds 00 being 1 or undefined. For countless applications, defining 00 as 1 is convenient.

a0 = 1

Shown below is an example of an discussion for a0=1 using one of the abovementioned exponent laws.

If one × to be = a(n+m)Thenan × a0 = a(n+0) = an

Thus, the only means for an to remain unchanged by multiplication, and this exponent law to stay true, is for a0 to be 1.

When an exponent is a fraction where the molecule is 1, the nth source of the basic is taken. Shown listed below is an instance with a fractional exponent where the numerator is not 1. It supplies both the ascendancy displayed, and the preeminence for multiplying index number with prefer bases questioned above. Keep in mind that the doyourpartparks.org can calculate fountain exponents, yet they need to be gone into into the doyourpartparks.org in decimal form.

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It is also feasible to compute index number with an unfavorable bases. Castle follow much the exact same rules together exponents with hopeful bases. Index number with an adverse bases increased to optimistic integers room equal come their confident counterparts in magnitude, however vary based upon sign. If the exponent is one even, positive integer, the worths will be equal regardless the a optimistic or an adverse base. If the exponent is an odd, hopeful integer, the result will again have actually the very same magnitude, but will it is in negative. While the rules because that fractional exponents with an unfavorable bases room the same, castle involve the usage of imaginary numbers due to the fact that it is not possible to take any type of root that a an unfavorable number. An example is detailed below for reference, yet please keep in mind that the doyourpartparks.org listed cannot compute imaginary numbers, and any inputs that result in an imagine number will certainly return the an outcome \"NAN,\" signifying \"not a number.\" The numerical equipment is essentially the same as the situation with a confident base, other than that the number should be denoted together imaginary.