Solution:
Given the expression:
[tex]\frac{y^9\cdot y^8}{y^4}[/tex]
The above expression can be further expressed as
[tex]\frac{y^9\times y^8}{y^4}[/tex]
From the laws of exponents,
[tex]\begin{gathered} a^x\times a^y=a^{(x+y)} \\ \frac{a^x}{a^y}=a^{(x-y)} \end{gathered}[/tex]
Thus, we have
[tex]\begin{gathered} \frac{y^9\times y^8}{y^4}=\frac{y^{(9+8)}}{y^4} \\ =\frac{y^{17}}{y^4} \\ recall\text{ that} \\ \frac{a^x}{a^y}=a^{(x-y)} \\ thus,\text{ we have} \\ \frac{y^{17}}{y^{4}}=y^{(17-4)} \\ \Rightarrow y^{13} \end{gathered}[/tex]
Hence, we have
[tex]y^{13}[/tex]
