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:
[tex]a^{-n} = \frac{1}{a^n}[/tex]
1.
Given the expression:
[tex]3^{-4}[/tex]
Apply the exponent rules:
[tex]\frac{1}{3^4} = \frac{1}{81}[/tex]
Therefore, the value of the given expression is, [tex]\frac{1}{81}[/tex].
2.
To find the value of the expression [tex]\frac{1}{4^3}[/tex]
then;
[tex]\frac{1}{4^3} = \frac{1}{64}[/tex]
Therefore, the value of the given expression is, [tex]\frac{1}{64}[/tex].
3.
Find the the value of the expression [tex]\frac{2}{4^3}[/tex]
then;
[tex]\frac{2}{4^3} = \frac{2}{64}[/tex]
Simplify:
[tex]\frac{1}{32}[/tex]
Therefore, the value of the given expression is, [tex]\frac{1}{32}[/tex].
4.
Given the expression:
[tex]K^{-3} = \frac{1}{27}[/tex]
we can write this as:
[tex]K^{-3} = \frac{1}{3^3}[/tex]
Apply the exponent rules:
[tex]K^{-3} = 3^{-3}[/tex]
On comparing both sides we have;
K = 3
Therefore, the value of K is, 3
5.
Given the expression:
[tex]3^N= \frac{1}{81}[/tex]
we can write this as:
[tex]3^N= \frac{1}{3^4}[/tex]
Apply the exponent rules:
[tex]3^N = 3^{-4}[/tex]
On comparing both sides we have;
N = 4
Therefore, the value of N is, -4
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
