Simplify: #((-24)/(-4))-:2+3*(-5+1)^2#?

Using PEDMAS
#(-24/-4)-:2+3(-5+1)^2#

#"P"->(+6)-:2+3(-4)^2#

#"E"->(6)-:2+3(16)#

#"D"->6/2+3(16)" "->" "3+3(16)#

#"M"->3+48#

#"A"->51#

#"S"->" not applicable"#

#(-24)/(-4)-:2+3(-5+1)^2#

The order of operations is parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right.

Simplify #(-5+1)#.

#(-24)/(-4)-:2+3(-4)^2#

Simplify #(-4)^2#.

#(-24)/(-4)-:2+3xx16#

Simplify #(-24)/(-4)#.

#24/4-:2+3xx16#

Simplify #24/4#.

#6-:2+3xx16#

Simplify #6-:2#.

#3+3xx16#

Simplify #3xx16#.

#3+48#

Simplify #3+48#.

#51#

To make the order of operations easier, count the number of terms first. Keep the terms separate.

EAch term must simplify to a single answer. The answers will be added or subtracted in the LAST step. You can work in different terms in the same step

Do the strongest operations first - the power and roots.

Then do multiplication and division.

If this order is to be changed, parentheses are used to indicate which must be done before the normal order.

#color(red)((-24)/(-4)-:2)" "color(blue)(+3(-5+1)^2)" has 2 terms"#
#"division addition"#

#color(red)((6-:2)" "color(blue)(+3(-4)^2)#

#color(red)((3)" "color(blue)(+3(16)#

#color(red)((3)" "color(blue)(+48)#

=#51#