Answer:
The correct option is D) -9/16
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Step-by-step explanation:
Given:
[tex]9x^{-5}y^{-2}[/tex]
Evaluate when x = -1 and y = 4
Solution:
When x = -1 and y = 4 we hane
[tex]9x^{-5}y^{-2}=9(-1)^{-5}(4)^{-2}[/tex]
Identity we have
[tex]x^{-a}=\dfrac{1}{x^{a}}[/tex]
As we know minus sign multiplied by odd number of times the number is multiplied and the assign remain same that is minus. Therefore,
[tex](-1)^{5}=-1\times -1\times -1\times -1\times -1\\(-1)^{5}=-1[/tex]
Now using the above identity we get
[tex]9x^{-5}y^{-2}=\dfrac{9}{(-1)^{5}}\times \dfrac{1}{(4)^{2}}[/tex]
[tex]9x^{-5}y^{-2}=\dfrac{9}{-1}\times\dfrac{1}{16}[/tex]
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
