What is the value of n in this equation: 2↑2 * 2↑n = (2↑4)↑3

Answer:The value of n in the given equation is; n = 10Step-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)↑3Using [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 -2Simplify:n = 10Therefore, the value of n is, 10