Question

Add as many pairs of parentheses () as you want to 2^1+3*4+5 anywhere in the expression to change the order of operations, then evaluate the new expression. [An example would be to try (2^1+3)*(4+5)]. Get the largest value that you can by putting parentheses in different places to change what gets evaluated first. Show your steps to calculate the value of your expression and justify why you think you have found the largest value.

PLEASE HELP

Answer 1

The largest value that you can get by putting parentheses in different places should be,

`2^(36) =6.87 * 10^(10)`

Solution-

Among all mathematical operations, power and factorial operation generates enormously big results.

So taking the power of all the remaining expressions,

`2^((1+3*4+5))`

After, power and factorial operations, multiplication and addition yield big results.

But, here before doing multiplication, adding 1, 3 and 4, 5 and then multiplying the both results, gives bigger number.

( ∵ 1+(3*4)+5 = 18, but (1+3)*(4+5)= 36 )

So,

`2^(((1+3)*(4+5)))`

`=2^((4*9))`

`=2^(36)`