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What is an exponent?
Exponentiation is a math operation, written as an, including the basic a and an exponent n. In the situation where n is a hopeful integer, exponentiation corresponds to repetitive multiplication that the base, n times.
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an = a × a × ... × a n times
The snucongo.org over accepts an unfavorable bases, yet does not compute imaginary numbers. It additionally does no accept fractions, however can be provided to compute spring exponents, as long as the exponents are input in your decimal form.
Basic exponent laws and also rules
When exponents that share the exact same base room multiplied, the exponents space 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 negative sign is removed by reciprocating the base and raising it come the positive exponent.
a(-n)= | 1 |
an |
EX: 2(-3) = 1 ÷ 2 ÷ 2 ÷ 2 | = | 1 |
8 |
EX: 2(-3)= | 1 |
23 |
8 |
When exponents that share the very same base are divided, the exponents space subtracted.
am |
an |
EX: | 22 |
24 |
16 |
4 |
22 |
24 |
22 |
4 |
When exponents are raised to an additional exponent, the exponents are multiplied.
(am)n = a(m × n)EX: (22)4 = 44 = 256(22)4 = 2(2 × 4) = 28 = 256
When multiply bases are raised 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 raised to one exponent, the exponent is spread to both bases.
( | a |
b |
bn |
EX: ( | 2 |
5 |
5 |
5 |
25 |
( | 2 |
5 |
52 |
25 |
When an exponent is 1, the base remains the same.
a1 = a
When an exponent is 0, the an outcome of the exponentiation of any type of base will always be 1, although somedebate surrounding 00 being 1 or undefined. For countless applications, specifying 00 as 1 is convenient.
a0 = 1
Shown listed below is an instance of an argument for a0=1 using among the abovementioned exponent laws.
If one × to be = a(n+m)Thenan × a0 = a(n+0) = an
Thus, the only way for an to stay unchanged through multiplication, and this exponent legislation to continue to be true, is for a0 to it is in 1.
When an exponent is a portion where the numerator is 1, the nth source of the basic is taken. Shown below is an example with a fountain exponent where the molecule is not 1. It uses both the preeminence displayed, as well as the rule for multiplying index number with favor bases debated above. Note that the snucongo.org deserve to calculate fountain exponents, but they need to be entered into the snucongo.org in decimal form.
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It is also possible to compute exponents with an unfavorable bases. Castle follow lot the same rules as exponents with hopeful bases. Index number with an adverse bases elevated to positive integers space equal come their hopeful counterparts in magnitude, however vary based upon sign. If the exponent is one even, optimistic integer, the values will be same regardless that a positive or an adverse base. If the exponent is one odd, confident integer, the an outcome will again have actually the very same magnitude, however will it is in negative. When the rules because that fractional exponents with an unfavorable bases room the same, they involve the use of imagine numbers since it is not feasible to take any root the a negative number. An instance is noted below because that reference, yet please keep in mind that the snucongo.org detailed cannot compute imagine numbers, and any inputs that result in an imaginary number will return the result "NAN," signifying "not a number." The numerical equipment is basically the exact same as the instance with a hopeful base, other than that the number should be denoted together imaginary.