Question

Simplify (8^4/10^4)^-1/4using rational exponents

Answer 1

`((8^4)/(10^4) )^{-(1)/(4) }` =
`(5)/(4)`

Explanation:

Explanation

Given

`((8^4)/(10^4) )^{-(1)/(4) }`

By using algebra formulas

`((a)/(b) )^(m) = (a^m)/(b^n)`

`((8^4)/(10^4) )^{-(1)/(4) } = \frac{(8^(4))^{(-1)/(4) } }{(10^(4) )^{(-1)/(4) } }`

`(a^(m) )^(n) = a^(mn)`

`\frac{(8^(4))^{(-1)/(4) } }{(10^(4) )^{(-1)/(4) } } = \frac{8^{4X(-1)/(4) } }{10^{4 X(-1)/(4) } }`

=
`(8^(-1) )/(10^(-1) )`

`= (10)/(8) \\= (5)/(4)`

Final answer:-

`((8^4)/(10^4) )^{-(1)/(4) }` =
`(5)/(4)`