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

 

 

 

This arithmetic with the exponents is within our capabilities.

 

 

 

let us now rearrange to get factors with common bases next to each other.

 

 

 

The rule for exponents which applies in this case is that when you multiply powers of the same base, you add the exponents. When you divide powers of the same base, you subtract the exponents. Even though we have some negative exponents, we can still add and subtract these numbers.

 

 

This gives us

 

 

We would be done except that the directions tell us to express our answer using only positive exponents. If a factor has a negative exponent, we move it across the fraction bar and that will change the sign on the exponent.

 

 

 

Usually, in a case like this, they will square the 3

 

top

return to problem 4