#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.

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