Practice with Exponents

Due to math content, this page has special requirements (including JavaScript) for full functionality.
With your current viewing scenario, it is not appearing and behaving as it is supposed to!
Please visit Dr. Carol J.V. Fisher's Homepage to learn what this site has to offer.
Watch the "Welcome" video to get started—hope to see you back here soon!

Dr. Carol J.V. Fisher's Homepage

For this exercise, you need ♥ INTERNET EXPLORER 6.0 and above, with MathPlayer installed.♥

PRACTICE WITH EXPONENTS

Jump right to the exercises!

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 .

When simplifying expressions involving exponent notation,
figure out the sign (plus or minus) of the expression first,
then figure out its size.

Recall that any even number (2, 4, 6, ...) of negative factors is positive.
Any odd number (1, 3, 5, ...) of negative factors is negative.

For example, consider (-2) 6 .
There are an even number (6) of negative factors, so the result is positive.
The size of the result is 26 =64 .
Thus, (-2) 6=64 .

As a second example, consider consider (-2) 5 .
There are an odd number (5) of negative factors, so the result is negative.
The size of the result is 25 =32 .
Thus, (-2) 5=-32 .

Since exponents are done before multiplication,
-2 4=(-1 )(24 )=-16 .

Be careful!
The numbers -2 4 and (-2) 4 represent different orders of operations,
and are different numbers!

Similarly, -2 3 and (-2) 3 represent different orders of operations,
but they result in the same number!

EXAMPLES:
(-2)³ = -8
-2³ = -8
(-2)⁴ = 16
-2⁴ = -16
If an expression is not defined, input "nd".