Algebra II: Getting Started -Identities and Properties
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, 34 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:
xm xn = x(n+m)
(xm)n = xmn for x 0, and
x-m = 1/xm
xm/xn = xm-n
(xy)n = xnyn (More text below video...)
<h2> Getting Started -Identities and Properties - Watch video (Algebra II)</h2> <p> video, AlgebraII, practice questions, quizzes, subject, math help,properties,fractional exponents,identities, example.</p> <p> introduced to fractional exponents following the definition of exponent, important identities and properties satisfied by integer exponentiation. </p>
Other useful lessons:
Evaluating numbers raised to fractional exponents
Simplifying expressions with exponents
Solving equations involving fractional exponents
(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 x1/4 i.e. with exponent of one-quarter (1/4). This means (x1/4)4 = x1/4*4= x1 = x. So,
          x1/4 = 4th root of x.
We can generalize and state:
A fractional exponent like 1/n means to take the nth root:
          x1/n = nx
E.g. 271/3 = 327 = 3.
Similarly a fractional exponent like m/n means to do the mth power, then take the nth root i.e.
          xm/n = nxm.
For example, 43/2 = 4 3*1/2 = (43) = (444) = (64) = 8.
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