Question

For any positive integers a and b, the operation ⓧ is defined as aⓧb=(2a-1)^b-1. what is the value of (2ⓧ2)ⓧ3?

Answer 1

The value of the given operation is 25.

Explanation:

We where given a rule of operation called
`\otimes` with the form

`a\otimes b=(2a-1)^(b-1)`

where a and b are positive integers. Then we where asked to calculate

`(2\otimes 2)\otimes 3`

In order to do it, we have to make two calculations, evaluating this operation properly each time... First we calculate the parentesis as it is the operation of higher hierarchy:

`(2\otimes 2)=(2*2-1)^(2-1)=(4-1)^1=3`

then, we replace that outcome in the second calculation

`(2\otimes 2)\otimes 3=3\otimes 3=(2*3-1)^(3-1)=(6-1)^2=5^2=25`

which is the value asked in the problem.