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A Power of a Power is POWERFUL!
The biggest thing you want to remember with this topic is that it is not the same as multiplying monomials.
If we once again look at the literal meaning behind the symbols it will all become clear.
Let's
take a look at some:
(x^3)^2 literally, this means (x^3)(x^3)
= x^6
(3r^4y)^3
which literally means
(3r^4y)(3r^4y)(3r^4y)
Now remember, we can rearrange these numbers using the
commutative property of multiplication,
then we can group the numbers and like bases using the associative
property of multiplication.
It
will look like this:
(3*3*3)(r^4*r^4*r^4)(y*y*y)
= or more simply
27r^12y^3
*NOW
here is the shorthand method.
When taking a power and raising it to a power, you simply MULTIPLY
the exponents.
Give these a try and then click the answer link to see if you were correct.
- (-2x^3)^5 = ?......answer
- -3x(2a^2)^3 = ? ........answer *remember that the -3x is NOT being raised to the third power here. We can tell this because it is not in the parentheses.
- (3r^4w)^4(r^3w^2)^9 = ?......answer Be sure to do this one on paper first. It is pretty complicated. Don't peek at the answer till you've tried it!!
