Question

Consider the expression. (StartFraction 2 m Superscript negative 1 baseline n Superscript 5 Baseline Over 3 m Superscript 0 Baseline n Superscript 4 Baseline EndFraction) squared What is the value of the expression if m = –5 and n = 3? Negative StartFraction 24 Over 25 EndFraction Negative StartFraction 4 Over 25 EndFraction StartFraction 4 Over 25 EndFraction StartFraction 24 Over 25 EndFraction

Answer 1

4/25

Explanation:

I just did the test

Answer 2

The correct option is option (3) 4 ÷ 25.

Explanation:

The expression in terms of m and n is:

`F(m,n)=[(2m^(-1)n^(5))/(3m^(0)n^(4))]^(2)`

Exponent rule of division:

`a^(x)/ a^(y)=a^(x-y)`

Compute the value of the expression for m = -5 and n = 3 as follows:

`F(m,n)=[(2m^(-1)n^(5))/(3m^(0)n^(4))]^(2)`

`F(-5,3)=[(2\csdot (-5)^(-1)\cdot (3)^(5))/(3\cdot (-5)^(0)\cdot (3)^(4))]^(2)`

`=\{(2)/(3)* [(-5)^(-1-0)* (3)^(5-4)}]\}^(2)\\\\=\{(2)/(3)* (-1)/(5)* 3\}^(2)\\\\=\{-(2)/(5)\}^(2)\\\\=(4)/(25)`

Thus, the correct option is option (3) 4 ÷ 25.