Question

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

Answer 1

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 = $a^b$          ......[1]

Given the expression: 2↑2 * 2↑n = (2↑4)↑3

Using [1] in the given expression is;

$(2^2) \cdot 2^n = (2^4)^3$

Using $a^n \cdot a^m = a^{n+m}$  and $(a^n)^m = a^{nm}$

we have;

$2^{2+n} = 2^{12}$

2 + n = 12                     [ Using $a^m = a^n$ ⇒ 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