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
