Question

Solve for x wen 9 to the power x divide by 81 to the power 2over x​

Answer 1

`{9}^(x) / {81}^{ (2)/(x) } = 1`

`{9}^(x) * {81}^{ ( - 2)/(x) } = 1`

`{9}^(x) * { ({9}^(2)) }^{ ( - 2)/(x) } = 1`

`{9}^(x) * {9}^{ ( - 4)/(x) } = 1`

`{9}^{(x - (4)/(x)) } = 1`

`{9}^(0 ) = 1 \: \: \: \: \: (known)`

Equating the exponents

`x - (4)/(x) = 0`

`\frac{ {x}^(2) - 4 }{x} = 0`

`{x}^(2) = 4 \\ x = + 2 \: or \: 2`