^ | = | ||
use e as base | |||
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What is an exponent?
Exponentiation is a mathematical operation, written as an, including the basic a and also an exponent n. In the situation where n is a positive integer, exponentiation synchronizes to repeated multiplication that the base, n times.
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an = a × a × ... × a n times
The hunterriverpei.com over accepts an unfavorable bases, however does not compute imaginary numbers. It likewise does not accept fractions, but can be supplied to compute fractional exponents, as long as the exponents room input in your decimal form.
Basic exponent laws and also rules
When exponents the share the very same base space multiplied, the exponents room added.
an × to be = 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 also raising it to the optimistic 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 room divided, the exponents room subtracted.
am |
an |
EX: | 22 |
24 |
16 |
4 |
22 |
24 |
22 |
4 |
When exponents are increased to another exponent, the exponents are multiplied.
(am)n = a(m × n)EX: (22)4 = 44 = 256(22)4 = 2(2 × 4) = 28 = 256
When multiplied bases are elevated to one exponent, the exponent is spread to both bases.
(a × b)n = one × bnEX: (2 × 4)2 = 82 = 64(2 × 4)2 = 22 × 42 = 4 × 16 = 64
Similarly, when divided bases are raised to one exponent, the exponent is dispersed to both bases.
( | a |
b |
bn |
EX: ( | 2 |
5 |
5 |
5 |
25 |
( | 2 |
5 |
52 |
25 |
When one exponent is 1, the base continues to be the same.
a1 = a
When an exponent is 0, the an outcome of the indices of any type of base will constantly be 1, return somedebate surrounds 00 gift 1 or undefined. For many applications, defining 00 together 1 is convenient.
a0 = 1
Shown below is an instance of an debate for a0=1 using one of the abovementioned exponent laws.
If one × am = a(n+m)Thenan × a0 = a(n+0) = an
Thus, the only way for an to remain unchanged by multiplication, and also this exponent law to stay true, is for a0 to be 1.
When an exponent is a fraction where the numerator is 1, the nth root of the base is taken. Shown below is an example with a fractional exponent wherein the molecule is no 1. It provides both the ascendancy displayed, and also the preeminence for multiplying index number with like bases discussed above. Keep in mind that the hunterriverpei.com can calculate fractional exponents, however they must be entered into the hunterriverpei.com in decimal form.
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It is also possible to compute exponents with negative bases. Castle follow lot the exact same rules as exponents with confident bases. Index number with an unfavorable bases raised to confident integers are equal to their hopeful counterparts in magnitude, yet vary based on sign. If the exponent is an even, hopeful integer, the worths will be same regardless that a optimistic or an unfavorable base. If the exponent is an odd, optimistic integer, the result will again have the very same magnitude, however will be negative. If the rules for fractional exponents with an adverse bases space the same, they involve the use of imagine numbers due to the fact that it is not feasible to take any root of a negative number. An instance is provided below for reference, however please note that the hunterriverpei.com noted cannot compute imagine numbers, and also any inputs that result in an imagine number will certainly 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 should be denoted together imaginary.