Starting with the expression:
[tex]\frac{45w^8}{9w^2}[/tex]Write the fraction as the product of 45/9 and the fraction involving the variable w:
[tex]\frac{45w^8}{9w^2}=\frac{45}{9}^{}\cdot\frac{w^8}{w^2}[/tex]Notice that 45/9=5. Then:
[tex]\frac{45}{9}\cdot\frac{w^8}{w^2}=5\cdot\frac{w^8}{w^2}[/tex]Recalling the laws of exponents:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]Then:
[tex]\begin{gathered} 5\cdot\frac{w^8}{w^2}=5\cdot w^{8-2} \\ =5\cdot w^6 \end{gathered}[/tex]Therefore:
[tex]\frac{45w^8}{5w^2}=5w^6[/tex]