Simplify {3}^(7y) * {81}^(8y) * {3}^(9) / {27}^(9y) ​

Question

Simplify


`{3}^(7y) * {81}^(8y) * {3}^(9) / {27}^(9y)`
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Answer 1

`3^(12y+9)`

Explanation:

→ Convert all integers to base 3

`3^(7y) *3^(4*8y)*3^(9) /3^(3*9y)`

→ Simplify

`3^(7y)*3^(32y) *3^(9) /3^(27y)`

→ Collect all the like terms

`3^(12y+9)`

Answer 2

`3^(7y) * 81^(8y) * 3^9 * 27^(-9y) = 3^(7y) * (3^4)^(8y) * 3^9 *(3^3)^(-9y)`

`=3^(7y) * (3)^(32y) * 3^9 *(3)^(-27y)\\\\=3^(7y +32y +9 -27y)\\\\=3^(12y+9)`

Tip :

`(1)/(27^(9y)) = 27^(-9y) = (3^3)^(-9y) = 3^(-27y)`