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

Answer:

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

Answer:

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:

$a^{-n} = \frac{1}{a^n}$

1.

Given the expression:  

$3^{-4}$

Apply the exponent rules:

$\frac{1}{3^4} = \frac{1}{81}$

Therefore,  the value of the given expression is, $\frac{1}{81}$.

2.

To find the value of the expression $\frac{1}{4^3}$

then;

$\frac{1}{4^3} = \frac{1}{64}$

Therefore, the value of the given expression is, $\frac{1}{64}$.

3.

Find the the value of the expression $\frac{2}{4^3}$

then;

$\frac{2}{4^3} = \frac{2}{64}$

Simplify:

$\frac{1}{32}$

Therefore, the value of the given expression is, $\frac{1}{32}$.

4.

Given the expression:

$K^{-3} = \frac{1}{27}$

we can write this as:

$K^{-3} = \frac{1}{3^3}$

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:

$3^N= \frac{1}{81}$

we can write this as:

$3^N= \frac{1}{3^4}$

Apply the exponent rules:

$3^N = 3^{-4}$

On comparing both sides we have;

N = 4

Therefore, the value of N is, -4