Question

\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }

Solve this ...
this is the question of laws of indices(exponent)​

Answer 1

5

Explanation:

Given expression:

`(6^(n+2)-6^n)/(6^(n+1)+6^n)`

`\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c`

`\implies (6^n6^2-6^n)/(6^n6^1+6^n)`

Factor:

`\implies (6^n(6^2-1))/(6^n(6^1+1))`

Cancel
`6^n` :

`\implies ((6^2-1))/((6^1+1))`

Simplify:

`\implies (36-1)/(6+1)`

`\implies (35)/(7)`

`\implies 5`