Answer:
The value of n in the given equation is; n = 10
Step-by-step explanation:
Exponent for a natural power b is defined as iterated multiplication, which Knuth denoted by a single up-arrow:
a↑b = [tex]a^b[/tex] ......[1]
Given the expression: 2↑2 * 2↑n = (2↑4)↑3
Using [1] in the given expression is;
[tex](2^2) \cdot 2^n = (2^4)^3[/tex]
Using [tex]a^n \cdot a^m = a^{n+m}[/tex] and [tex](a^n)^m = a^{nm}[/tex]
we have;
[tex]2^{2+n} = 2^{12}[/tex]
2 + n = 12 [ Using [tex]a^m = a^n[/tex] ⇒ m =n ]
Subtract 2 to both sides of an equation:
2 + n - 2 = 12 -2
Simplify:
n = 10
Therefore, the value of n is, 10
