Question

I need help with number 12 and can you please write your final answer using only positive exponents

Answer 1

Given the expression:

`(y^9\cdot y^8)/(y^4)`

The above expression can be further expressed as

`(y^9* y^8)/(y^4)`

From the laws of exponents,

`\begin{gathered} a^x* a^y=a^((x+y)) \\ (a^x)/(a^y)=a^((x-y)) \end{gathered}`

Thus, we have

`\begin{gathered} (y^9* y^8)/(y^4)=(y^((9+8)))/(y^4) \\ =(y^(17))/(y^4) \\ recall\text{ that} \\ (a^x)/(a^y)=a^((x-y)) \\ thus,\text{ we have} \\ (y^(17))/(y^(4))=y^((17-4)) \\ \Rightarrow y^(13) \end{gathered}`

Hence, we have

`y^(13)`