Question

Fractional index
Without using mathematical table simplify the following
(16/81)^-3/4

Answer 1

`(27)/(8)`

Explanation:

using the rules of exponents/ radicals

•
`((a)/(b)) ^(-m)` =
`((b)/(a)) ^(m)`

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

then

`((16)/(81)) ^{-(3)/(4) }`

=
`((81)/(16)) ^{(3)/(4) }`

=
`\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }`

=
`(3^3)/(2^3)`

=
`(27)/(8)`