Question

Write down the value of 27^-1/3

Answer 1

`(1)/(3)`

Explanation:

using the rules of exponents

•
`a^(-m)` =
`(1)/(a^(m) )`

•
`a^{(1)/(n) }` =
`\sqrt[n]{a}`

then

`27^{-(1)/(3) }`

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

=
`\frac{1}{\sqrt[3]{27} }`

=
`(1)/(3)`

Answer 2

`(1)/(3)`

Explanation:

Given:

`27^{-(1)/(3)}`

Rewrite 27 as 3³:

`\implies (3^3)^{-(1)/(3)}`

`\textsf{Apply the exponent rule} \quad (a^b)^c=a^(bc):`

`\implies 3^{3 *-(1)/(3)}`

`\implies 3^{-(3)/(3)}`

`\implies 3^(-1)`

`\textsf{Apply the exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (1)/(3^1)`

`\implies (1)/(3)`