Question

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.

Answer 1

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

Answer 2

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

Step-by-step explanation:

Using exponent rule:

`a^(-n) = (1)/(a^n)`

1.

Given the expression:

`3^(-4)`

Apply the exponent rules:

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

Therefore, the value of the given expression is,
`(1)/(81)`.

2.

To find the value of the expression
`(1)/(4^3)`

then;

`(1)/(4^3) = (1)/(64)`

Therefore, the value of the given expression is,
`(1)/(64)`.

3.

Find the the value of the expression
`(2)/(4^3)`

then;

`(2)/(4^3) = (2)/(64)`

Simplify:

`(1)/(32)`

Therefore, the value of the given expression is,
`(1)/(32)`.

4.

Given the expression:

`K^(-3) = (1)/(27)`

we can write this as:

`K^(-3) = (1)/(3^3)`

Apply the exponent rules:

`K^(-3) = 3^(-3)`

On comparing both sides we have;

K = 3

Therefore, the value of K is, 3

5.

Given the expression:

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

we can write this as:

`3^N= (1)/(3^4)`

Apply the exponent rules:

`3^N = 3^(-4)`

On comparing both sides we have;

N = 4

Therefore, the value of N is, -4