#1 What is the value of the expression 7–3? Answers: A. –21B. 1/343 C. 1/343 D. 343

#2What is the value of the expression 1/5^-5? Answers: A. 1/3125 B. 1/25 C. 25 D. 3125

#3What is the value of the expression 2/4^-3? Answers: A. 1/32 B. 1/6 C. 128 D. 256

#4 What value of k solves the equation? K^-2=1/64 Answers: A. 1/8 B. 8 C. 32 D. 128

#5 What value of n solves the equation? 4^N= 1/64 Answers: A. –3 B. 3 C. 16 D. 256

\( \#1\ \ \ 7^{-3}= \frac{1}{7^3} = \frac{1}{343}\ \ \ \Rightarrow\ \ \ Ans. \ C\\ \\ \#2\ \ \ \frac{1}{5^{-5}}=5^5=3125\ \ \ \Rightarrow\ \ \ \ Ans. \ D\\ \\ \#3\ \ \ \frac{2}{4^{-3}}=2\cdot4^{3}=2\cdot 64=128\ \ \ \Rightarrow\ \ \ Ans. \ C\\ \\\#4\ \ \ K^{-2}= \frac{1}{64} \ \ \Rightarrow\ \ \ \frac{1}{K^2} = \frac{1}{64}\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K^2=64 \ \ \Rightarrow\ \ K=8\ \ \Rightarrow\ \ Ans. \ B\\ \\ \)

\( \#5\ \ \ 4^N= \frac{1}{64}\ \ \Rightarrow\ \ \ 4^N=4^{-3}\ \ \ \Rightarrow\ \ \ N=-3\ \ \ \Rightarrow\ \ \ Ans. \ A \)

First question

The given expression is

\( 7^{-3} \)

Which can also be written as

\( \frac{1}{7^3}= \frac{1}{343} \)

Therefore the correct option is C.

2.

The given expression is

\( \frac{1}{5^{-5}} \)

Which can also be written as

\( 5^5 = 3125 \)

So the correct option is D

3.

The given expression is

\( \frac{2}{4^{-3}} \)

Which can also be written as

\( 2*4^3 = 2* 64=128 \)

And the correct option is C

4.

The given equation is

\( k^{-2} = \frac{1}{64} \\ k^2 = 64 \\ k^2 = 8^2 \\ k=8 \)

So the correct option is B

5.

The given equation is

\( 4^N = \frac{1}{64} \\ 4^N = 4^{-3} \\ N =-3 \)

And the correct option is A.