Answer
[tex]\frac{24u^7v^5}{48uv^8}=\frac{u^6}{2v^3}[/tex]
Solution
- The question asks us to simplify the following expression:
[tex]\frac{24u^7v^5}{48uv^8}[/tex]
- 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:
[tex]\begin{gathered} \text{Law 1:} \\ \frac{a^b}{a^c}=a^{b-c} \\ \\ \text{Law 2:} \\ \frac{abc}{\text{xya}}=\frac{a}{x}\times\frac{b}{y}\times\frac{c}{z} \\ \\ \text{Law 3:} \\ a^{-b}=\frac{1}{a^b} \end{gathered}[/tex]
- Now that we have the laws of exponents we require, we can proceed to solve the question.
- This is done below:
[tex]\begin{gathered} \frac{24u^7v^5}{48uv^8} \\ \\ \text{Apply Law 2:} \\ \frac{24u^7v^5}{48uv^8}=\frac{24}{48}\times\frac{u^7}{u}\times\frac{v^5}{v^8} \\ \\ \text{Apply Law 1 } \\ \frac{24}{48}\times\frac{u^7}{u}\times\frac{v^5}{v^8}=\frac{24}{24\times2}\times u^{7-1}\times v^{5-8} \\ \\ =\frac{1}{2}\times u^6\times v^{-3} \\ \\ \therefore\frac{24u^7v^5}{48uv^8}=\frac{1}{2}\times u^6\times v^{-3} \\ \\ \text{But we are told to keep all exponents positive, thus, we should apply Law 3 to }v^{-3} \\ \\ \frac{1}{2}\times u^6\times v^{-3}=\frac{1}{2}\times u^6\times\frac{1}{v^3}=\frac{u^6}{2v^3} \\ \\ \frac{24u^7v^5}{48uv^8}=\frac{u^6}{2v^3} \end{gathered}[/tex]
Final Answer
[tex]\frac{24u^7v^5}{48uv^8}=\frac{u^6}{2v^3}[/tex]
