Respuesta :
Answer:
The correct option is option (3) 4 ÷ 25.
Step-by-step explanation:
The expression in terms of m and n is:
[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]
Exponent rule of division:
[tex]a^{x}\div a^{y}=a^{x-y}[/tex]
Compute the value of the expression for m = -5 and n = 3 as follows:
[tex]F(m,n)=[\frac{2m^{-1}n^{5}}{3m^{0}n^{4}}]^{2}[/tex]
[tex]F(-5,3)=[\frac{2\csdot (-5)^{-1}\cdot (3)^{5}}{3\cdot (-5)^{0}\cdot (3)^{4}}]^{2}[/tex]
[tex]=\{\frac{2}{3}\times [(-5)^{-1-0}\times (3)^{5-4}}]\}^{2}\\\\=\{\frac{2}{3}\times \frac{-1}{5}\times 3\}^{2}\\\\=\{-\frac{2}{5}\}^{2}\\\\=\frac{4}{25}[/tex]
Thus, the correct option is option (3) 4 ÷ 25.
