Basic Exponent Practice with Fractions

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BASIC EXPONENT PRACTICE WITH FRACTIONS

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The concepts for this exercise are summarized below. For a complete discussion, read the text.
MathPlayer is only required for the concept discussion; it is not required for the web exercise.

DEFINITIONS: properties of exponents
base; exponent; power	Let x∈ℝ . In the expression xn , x is called the *base* and n is called the *exponent* or the *power*.
positive integers	If n∈{1 ,2,3,... } , then xn =x⋅x⋅ x⋅...⋅x , where there are n factors in the product. In this case, xn is just a shorthand for repeated multiplication. Note that x1 =x for all real numbers x .
zero	If x≠0 , then x0 =1 . The expression 00 is not defined.
negative integers	If n∈{1 ,2,3,... } and x≠0 , then x- n=1 xn =1x ⋅x⋅x⋅ ...⋅x , where there are n factors in the product. In particular, x- 1=1 x1 =1x for all nonzero real numbers x . That is, x-1 is the reciprocal of x .

With fractions, it looks like this:

(a b)- 1=1 ab =1÷ ab= 1⋅b a=b a

That is, the reciprocal of ab is ba .

Now that you've mired through this calculation once,
you'll never have to do it this long way again.

When a fraction is raised to the -1 power, it just flips.
The numerator becomes the new denominator, and the denominator becomes the new numerator.

EXAMPLES:
(2/3)^-1 = 3/2
(2/3)⁰ = 1
(2/3)¹ = 2/3
(-2/3)^-1 = -3/2
5^-1 = 1/5
(-5)^-1 = -1/5
(1/3)^-1 = 3
(-1/3)^-1 = -3