1. what is the value of the expression 3^-4? . a) -81. b) -12. c) -1/81. d) 1/81. 2. what is the value of the expression 1/4^3? . a) 12. b) 64. c) 1/64. d) 1/12. 3. what is the value of the expression 2/4^3? . a) 1/32. b) 1/6. c) 128. d) 256. 4. what value of k solves the equation, k^-3=1/27? . a) -81. b) -9. c) -3. d) 3. 5. what value of n solves the equation, 3^n=1/81. a) -243. b) -27. c) -4. d) 3.

1.

Option d is correct

2.

Option c is correct

3.

Option a is correct

4.

Option d is correct

5.

Option c is correct

Explanation:

Using exponent rule:

1.

Given the expression:  

Apply the exponent rules:

Therefore,  the value of the given expression is, .

2.

To find the value of the expression

then;

Therefore, the value of the given expression is, .

3.

Find the the value of the expression

then;

Simplify:

Therefore, the value of the given expression is, .

4.

Given the expression:

we can write this as:

Apply the exponent rules:

On comparing both sides we have;

K = 3

Therefore, the value of K is, 3

5.

Given the expression:

we can write this as:

Apply the exponent rules:

On comparing both sides we have;

N = 4

Therefore, the value of N is, -4

1. option d

2. option c

3. option a

4. option d

5. option c

Step-by-step explanation:

1.

3^(-4) = 1/(3^4) = 1/81

2.

1/(4^3) = 1/64

3.

2/(4^3) = 2/64 = 1/32

4.

K^(-3) = 1/27  

1/(K^3) = 1/27  

27 = K^3

∛27 = K

3 = K

5.

3^N = 1/81

ln (3^N) = ln (1/81)

N*ln(3) = ln (1/81)

N =   ln (1/81)/ln(3)

N = -4

the answer is 3/2 and for decimal: 1.5

hope i

-lavira: )