Question

Simplify using exponents 45w^8 / 9w^2

Answer 1

Starting with the expression:

`(45w^8)/(9w^2)`

Write the fraction as the product of 45/9 and the fraction involving the variable w:

`(45w^8)/(9w^2)=(45)/(9)^{}\cdot(w^8)/(w^2)`

Notice that 45/9=5. Then:

`(45)/(9)\cdot(w^8)/(w^2)=5\cdot(w^8)/(w^2)`

Recalling the laws of exponents:

`(a^n)/(a^m)=a^(n-m)`

Then:

`\begin{gathered} 5\cdot(w^8)/(w^2)=5\cdot w^(8-2) \\ =5\cdot w^6 \end{gathered}`

Therefore:

`(45w^8)/(5w^2)=5w^6`