Question

(27)n/3×(8)-n/6 ÷(162)-n/2

Answer 1

Hi ,

( 27 )^n/3 × ( 8 )^-n/6 × ÷ ( 162 )^-n/2

= ( 3³ )^n/3 × ( 2³ )^-n/6 ÷ ( 2×9² )^-n/2

= [3^3n/3×2^(-3n )/6]/[2^-n/2× 9^-2n/2]

= [3ⁿ × 2^-n/2 ]/[ 2^-n/2 × 9^-n ]

After cancellation ,

= 3ⁿ × 9ⁿ

= 3ⁿ × ( 3² )ⁿ

= 3ⁿ × 3^2n

= 3^ n + 2n

= 3^ 3n

Or

= 27ⁿ

I hope this helps you.

: )