^=
use e together base
*

RelatedScientific rewildtv.com | log in rewildtv.com | source rewildtv.com

What is an exponent?

Exponentiation is a mathematical operation, created as an, including the basic a and an exponent n. In the instance where n is a hopeful integer, exponentiation synchronizes to recurring multiplication the the base, n times.

You are watching: What is 2 to the 6 power

an = a × a × ... × a n times

The rewildtv.com over accepts negative bases, yet does no compute imaginary numbers. It likewise does no accept fractions, yet can be supplied to compute fractional exponents, as lengthy as the exponents room input in their decimal form.

Basic exponent laws and also rules

When exponents the share the very same base are multiplied, the exponents are 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 eliminated by reciprocating the base and also raising it to 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 the share the exact same base are divided, the exponents room 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 index number are increased to one more 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 increased to one exponent, the exponent is spread to both bases.

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

Similarly, when split bases are increased to an 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 an exponent is 0, the result of the exponentiation of any base will always be 1, although somedebate surrounds 00 being 1 or undefined. For numerous applications, defining 00 together 1 is convenient.

a0 = 1

Shown below is an instance of an debate for a0=1 using among the previously mentioned exponent laws.

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

Thus, the only method for an to continue to be unchanged by multiplication, and this exponent legislation to remain true, is because that a0 to it is in 1.

When an exponent is a portion where the molecule is 1, the nth source of the base is taken. Shown listed below is an instance with a fountain exponent whereby the numerator is no 1. It uses both the preeminence displayed, and the dominance for multiplying index number with like bases debated above. Note that the rewildtv.com have the right to calculate fractional exponents, yet they need to be gotten in into the rewildtv.com in decimal form.

See more: How Many Valence Electrons Are Present In Silicon (Si) Have?

*

It is also feasible to compute exponents with an adverse bases. They follow lot the exact same rules together exponents with hopeful bases. Index number with negative bases raised to positive integers space equal to their positive counterparts in magnitude, but vary based on sign. If the exponent is one even, hopeful integer, the values will be same regardless the a hopeful or an adverse base. If the exponent is one odd, confident integer, the result will again have the very same magnitude, yet will be negative. When the rules for fractional index number with an adverse bases room the same, lock involve the use of imagine numbers because it is not feasible to take any kind of root of a an adverse number. An instance is detailed below for reference, but please keep in mind that the rewildtv.com listed cannot compute imagine numbers, and also any input that result in an imaginary number will return the an outcome "NAN," signifying "not a number." The numerical systems is essentially the exact same as the case with a confident base, other than that the number have to be denoted as imaginary.