Question

Find the value of (1³+2³+3³)^-3/2​

Answer 1

`(1)/(216)`

Explanation:

Using the rule of exponents

`a^(-m)` ⇔
`(1)/(a^(m) )`

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

Evaluate the parenthesis

1³ + 2³ + 3³ = 1 + 8 + 27 = 36 , then

`(36)^{-(3)/(2) }`

=
`\frac{1}{36^{(2)/(3) } }`

=
`(1)/((√(36))^3 )`

=
`(1)/(6^(3) )`

=
`(1)/(216)`