4. Simplify. Express your answer using all positive exponents.

 

 

The point of this problem is to use the rules for exponents. Since the expression inside the parentheses and the expression outside the parentheses are both simplified, we will need to remove the parentheses if we want to get anywhere. When you have a power on top of the parentheses you will need to raise all of the factors inside the parentheses to that power. Since some of the factors inside the parentheses have powers of their own, you will be raising a power to a power when you raise all of the factors inside the parentheses to the power on top of the parentheses. When you raise a power to a power, you multiply the powers.

As a result of all of these considerations, multiply all of the powers inside the parentheses, even the invisible powers of 1, times the power on top of the parentheses

 

You may find it helpful to move the factors with negative exponents across the fraction bar to change the signs on the exponents.

 

Now that all of the exponents are positive, we can spread out the factors.

You may not have to take this step and spread out the factors, but if you cold at least imagine what it would look like if you did, it will help to let you know how to proceed. After cancelling the factors which will cancel if we do this, we assemble the surviving factors and get

 

 

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