Question

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

Answer 1

The value of n in the given equation is; n = 10

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