Have you ever tried to multiply a power by a power when there is a monomial? Take a look at this dilemma.
This is a monomial expression that is being raised to the third power. Do you know how to simplify this expression?
Pay attention and you will know how to complete this dilemma by the end of the Concept.
We have raised monomials to a power, products to a power, and quotients to a power. You can see that exponents are a useful tool in simplifying expressions. If you follow the rules of exponents, the patterns become clear. We have already seen powers taken to a power. For example, look at the quotient:
If you focus on just the numerator, you can see that . You can get the exponent 28 by multiplying 7 and 4. This is an example of the Power of a Power Property which says for any nonzero numbers and and any integer :
Here is one.
Take a look at this one.
Apply the Power of a Power Property to each example.
Now let's go back to the dilemma from the beginning of the Concept.
Next, we have to take each part of the monomial and raise it to the third power.
Now we can put it altogether.
This is our solution.
Here is one for you to try on your own.
First, we are going to separate each part of the monomial and raise it to the fourth power.
Our final answer is .
Directions: Simplify each monomial expression by applying the Power of a Power Property.