Question

Evaluate the numerical expretion

I need help on this one

Answer 1

4/5

Explanation:

(5/4 )^(-1/5) is the same as (5^(-1/5) ) / (4^(-1/5)

which is the same as 4^(1/5) / 5^(1/5)

which is the same as (4/5)^1/5

so the result is this

(4/5)^1/5 * (4/5)^4/5 = (4/5)^(1/5 + 4/5) = (4/5)^1 = 4/5

Answer 2

`\sf (4)/(5)`

Explanation:

Exponent rule:

`\sf \boxed{\bf \left((a)/(b)\right)^(-m)= \left( (b)/(a)\right)^m}`

`\sf \left((5)/(4)\right)^{(-1)/(5)}*\left((4)/(5)\right)^{(4)/(5)}=\left((4)/(5)\right)^{(1)/(5)}*\left((4)/(5)\right)^{(4)/(5)}`

In exponent multiplication, if bases are same, add the exponents.

`\sf \boxed{\bf a^(m)*a^(n)=a^(m+n)}`

`\sf =\left((4)/(5)\right)^{(1)/(5)+(4)/(5)}\\\\=\left((4)/(5)\right)^{(5)/(5)}\\\\=\left((4)/(5)\right)^1\\\\=(4)/(5)`