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Apply all relevant properties of exponents to simplify the following expression.assume all variables are nonzero all exponents entered should be positive

Apply all relevant properties of exponents to simplify the following expression.assume-example-1
User Gmoss
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1 Answer

5 votes

Answer


(24u^7v^5)/(48uv^8)=(u^6)/(2v^3)

Solution

- The question asks us to simplify the following expression:


(24u^7v^5)/(48uv^8)

- In order to solve this, we need to know some laws of exponents to help us with the solution. The relevant laws of exponents for this question are given below:


\begin{gathered} \text{Law 1:} \\ (a^b)/(a^c)=a^(b-c) \\ \\ \text{Law 2:} \\ \frac{abc}{\text{xya}}=(a)/(x)*(b)/(y)*(c)/(z) \\ \\ \text{Law 3:} \\ a^(-b)=(1)/(a^b) \end{gathered}

- Now that we have the laws of exponents we require, we can proceed to solve the question.

- This is done below:


\begin{gathered} (24u^7v^5)/(48uv^8) \\ \\ \text{Apply Law 2:} \\ (24u^7v^5)/(48uv^8)=(24)/(48)*(u^7)/(u)*(v^5)/(v^8) \\ \\ \text{Apply Law 1 } \\ (24)/(48)*(u^7)/(u)*(v^5)/(v^8)=(24)/(24*2)* u^(7-1)* v^(5-8) \\ \\ =(1)/(2)* u^6* v^(-3) \\ \\ \therefore(24u^7v^5)/(48uv^8)=(1)/(2)* u^6* v^(-3) \\ \\ \text{But we are told to keep all exponents positive, thus, we should apply Law 3 to }v^(-3) \\ \\ (1)/(2)* u^6* v^(-3)=(1)/(2)* u^6*(1)/(v^3)=(u^6)/(2v^3) \\ \\ (24u^7v^5)/(48uv^8)=(u^6)/(2v^3) \end{gathered}

Final Answer


(24u^7v^5)/(48uv^8)=(u^6)/(2v^3)

User Janhartmann
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