(√6)²ⁿ+⁴ =216
I hv solved this sum like this -

(6²)²ⁿ+⁴ = 6³

6⁴ⁿ+8= 6³

As bases are same ; powers will also be same .

4n+8 = 3

4n= -5

Therefore ,n= -5/4
Can you please guide me where I have went wrong and why??

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Solution

$open parentheses square root of 6 close parentheses to the power of 2 n plus 4 space end exponent equals space 216 a s space w e space k n o w space t h a t space square root of bold 6 bold equals bold 6 to the power of bold 1 over bold 2 end exponent bold italic b bold italic u bold italic t bold space bold italic h bold italic e bold italic r bold italic e bold space bold italic y bold italic o bold italic u bold space bold italic w bold italic r bold italic o bold italic t bold italic e bold space bold 6 to the power of bold 2 bold comma bold space bold italic s bold italic o bold space bold italic t bold italic h bold italic i bold italic s bold space bold italic i bold italic s bold space bold italic y bold italic o bold italic u bold italic r bold space bold italic m bold italic i bold italic s bold italic t bold italic a bold italic k bold italic e. s o space open parentheses square root of 6 close parentheses to the power of 2 n plus 4 space end exponent space equals space open parentheses 6 to the power of 1 half end exponent close parentheses to the power of 2 n plus 4 end exponent space space open parentheses 6 to the power of 1 half end exponent close parentheses to the power of 2 n plus 4 end exponent equals space 6 to the power of fraction numerator 2 n plus 4 over denominator 2 end fraction end exponent equals 6 to the power of n plus 2 end exponent n o w space o u r space g i v e n space e q u a t i o n space i s space 6 to the power of n plus 2 space end exponent equals 6 cubed n o w space b y space c o m p a r i n g space e x p o n e n t s n space plus 2 space equals space 3 n space equals space 1 space t h i s space i s space t h e space c o r r e c t space a n s w e r.$

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