Question

The value of the expression 16-^3/4 is___
8
1/8
-6
6
1/40
1/64

Answer 1

`(1)/(8)`

Explanation:

Using the rules of exponents

•
`a^(-m)` ⇔
`(1)/(a^(m) )`

•
`a^{(m)/(n) }` ⇔
`\sqrt[n]{a^(m) }`

Hence

`16^{-(3)/(4) }` =
`\frac{1}{16^{(3)/(4) } }`

=
`\frac{1}{\sqrt[4]{16^(3) } }` =
`(1)/(2^(3) )` =
`(1)/(8)`