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

If the definition of $\otimes$ is $a\otimes b=(2a-1)^{b-1}$, then

$2\otimes2=(2\cdot2-1)^{2-1}=3^1=3$
$(2\otimes2)\otimes3=3\otimes3=(2\cdot3-1)^{3-1}=5^2=25$

Answer 2

Answer:

The value of the given operation is 25.

Step-by-step 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.