Getting Started -Identities and Properties

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: � x^m xⁿ = x^(n+m) � (x^m)ⁿ = x^mn for x 0, and � x^-m = 1/x^m � x^m/xⁿ = x^m-n � (xy)ⁿ = xⁿyⁿ (More text below video...)

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 x^1/4 i.e. with exponent of one-quarter (1/4). This means (x^1/4)4 = x^1/4*4= x¹ = 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 =

(4³) =

(4�4�4) =

(64) = 8.

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