Question

Simplify the expression to the lowest terms: (〖√(10^2−4^3 )〗^ −3^2 )

Answer 1

It should be
`\sqrt{(1)/(216) }` or
`(1)/(6√(6) )` (they're both the same thing, one is just more simplified than the other) unless I misread the question somehow.

Explanation:

Simplify

`(√(10^2-4^3) )^{(-3)/(2) }`

`√(100-64) ^{(-3)/(2) }`

`√(36) ^(-3)/(2)`

`(6)^(-3)/(2)`

Now, using the fractional exponent rule, we know this is the same as:

`\sqrt{6^(-3) }`

`\sqrt{(1)/(216) }`