This is a free lesson from our course in Algebra II
In this lesson, you'll be introduced to fractional exponents following the definition of exponent,
important identities and properties satisfied by integer exponentiation. Simply
saying the exponent of a number says how many times to multiply the number.For example,
3^{4} means to multiply 3 itself 4 times, where 3 is the base and the 4
called the exponent. Both the base and the exponent can be either a number or a
variable. The rules of exponents to remember are:
• x^{m}x^{n} = x^{(n+m)}
• (x^{m})^{n} = x^{mn} for x
0, and
• x^{m} = 1/x^{m}
• x^{m}/x^{n} = x^{mn}
• (xy)^{n} = x^{n}y^{n}(More text below video...)
(Continued from above) Moreover while
addition; multiplication is commutative and associative, but exponentiation is not.
Now, let's look at what happens when we write x^{1/4} i.e. with
exponent of onequarter (1/4). This means (x^{1/4})4 = x^{1/4*4}=
x^{1} = x. So, x^{1/4}
= 4^{th} root of x.
We can generalize and state:
A fractional exponent like 1/n means to take the n^{th} root: x^{1/n}
= ^{n}x
E.g. 27^{1/3} = ^{3}27
= 3.
Similarly a fractional exponent like m/n means to do the m^{th}
power, then take the n^{th} root i.e. x^{m/n}
= ^{n}x^{m}.
For example, 4^{3/2} = 4 ^{3*1/2} =
(4^{3})
=
(4×4×4)
=
(64)
= 8.
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