Question

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Answer 1

Simplifying the expression gives;

`(1)/(3^5)`

Step-by-step explanation:

Given the expression:

`(3^(-9)\cdot3^(12))/(3^6\cdot3^2)`

Applying the rules of exponent;

`\begin{gathered} (3^(-9)\cdot3^(12))/(3^6\cdot3^2)=(3^(-9+12))/(3^(6+2))=(3^3)/(3^8) \\ \end{gathered}`

Solving further;

`(3^3)/(3^8)=3^3\cdot3^(-8)=3^(3-8)=3^(-5)=(1)/(3^5)`

Therefore, simplifying the expression gives;

`(1)/(3^5)`