Question

9-^1/2 27^-2/3 evaluate

Answer 1

`(1)/(27)`

Explanation:

Using the rules of exponents/ radicals

`a^(-m)` =
`(1)/(a^(m) )`

`a^{(m)/(n) }` =
`\sqrt[n]{a^(m) }`

Given

`9^{-(1)/(2) }` ×
`27^{-(2)/(3) }`

=
`\frac{1}{9^{(1)/(2) } }` ×
`\frac{1}{27^{(2)/(3) } }`

=
`(1)/(√(9) )` ×
`\frac{1}{\sqrt[3]{27^(2) } }`

=
`(1)/(3)` ×
`(1)/(3^(2) )`

=
`(1)/(3)` ×
`(1)/(9)`

=
`(1)/(27)`