Answer :
[tex]\#1\ \ \ 7^{-3}= \frac{1}{7^3} = \frac{1}{343}\ \ \ \Rightarrow\ \ \ Ans.\ C\\ \\ \#2\ \ \ \frac{1}{5^{-5}}=5^5=3125\ \ \ \Rightarrow\ \ \ \ Ans.\ D\\ \\ \#3\ \ \ \frac{2}{4^{-3}}=2\cdot4^{3}=2\cdot 64=128\ \ \ \Rightarrow\ \ \ Ans.\ C\\ \\\#4\ \ \ K^{-2}= \frac{1}{64} \ \ \Rightarrow\ \ \ \frac{1}{K^2} = \frac{1}{64}\\\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K^2=64 \ \ \Rightarrow\ \ K=8\ \ \Rightarrow\ \ Ans.\ B\\ \\ [/tex]
[tex]\#5\ \ \ 4^N= \frac{1}{64}\ \ \Rightarrow\ \ \ 4^N=4^{-3}\ \ \ \Rightarrow\ \ \ N=-3\ \ \ \Rightarrow\ \ \ Ans.\ A[/tex]
[tex]\#5\ \ \ 4^N= \frac{1}{64}\ \ \Rightarrow\ \ \ 4^N=4^{-3}\ \ \ \Rightarrow\ \ \ N=-3\ \ \ \Rightarrow\ \ \ Ans.\ A[/tex]
First question
The given expression is
[tex]7^{-3}[/tex]
Which can also be written as
[tex]\frac{1}{7^3}= \frac{1}{343}[/tex]
Therefore the correct option is C.
2.
The given expression is
[tex]\frac{1}{5^{-5}}[/tex]
Which can also be written as
[tex]5^5 = 3125[/tex]
So the correct option is D
3.
The given expression is
[tex]\frac{2}{4^{-3}}[/tex]
Which can also be written as
[tex]2*4^3 = 2* 64=128[/tex]
And the correct option is C
4.
The given equation is
[tex]k^{-2} = \frac{1}{64} \\ k^2 = 64 \\ k^2 = 8^2 \\ k=8[/tex]
So the correct option is B
5.
The given equation is
[tex]4^N = \frac{1}{64} \\ 4^N = 4^{-3} \\ N =-3[/tex]
And the correct option is A .