5.The steps for simplifying ((rt^3)/(rtw))^4 are shown below.Assume that no denominator equals zero Match theproperties to the steps they justify. Step 1 ((rt^3)/(rtw))^4=((rt^3)^4)/((rtw)^4)underline ( ) Step 2 ((rt^3)^4)/((rtw)^4)=(r^4(t^3)^4)/(r^4)t^(4w^4)underline ( ) Step 3 (r^4(t^3)^4)/(r^4)t^(4w^4)=(r^4t^12)/(r^4)t^(4w^4) Step 4 (r^4t^12)/(r^4)t^(4w^4)=(t^8)/(w^4) __ A Product of Powers B Power of a Product C Distributive Property D Quotient of Powers E Power of a Power F Power of a Quotient

## Step 1<br />The first step involves applying the power of a quotient rule. This rule states that the power of a quotient is equal to the quotient of the powers. In this case, the quotient is \( \frac{rt^{3}}{rtw} \) and the power is 4. Therefore, the power of the quotient is \( \frac{(rt^{3})^{4}}{(rtw)^{4}} \).<br /><br />## Step 2<br />The second step involves applying the power of a product rule. This rule states that the power of a product is equal to the product of the powers. In this case, the product is \( rt^{3} \) and the power is 4. Therefore, the power of the product is \( r^{4}(t^{3})^{4} \).<br /><br />## Step 3<br />The third step involves applying the product of powers rule. This rule states that the product of powers is equal to the power of the product. In this case, the product is \( r^{4}t^{4} \) and the power is 4. Therefore, the product of powers is \( r^{4}t^{12} \).<br /><br />## Step 4<br />The fourth step involves applying the quotient of powers rule. This rule states that the quotient of powers is equal to the power of the quotient. In this case, the quotient is \( \frac{t^{12}}{t^{4}} \) and the power is 4. Therefore, the quotient of powers is \( \frac{t^{8}}{w^{4}} \).