# simplify the following  `(36*3 - 2) 3 -: 3 - 2`   `(2/5)3 (2/5)-2`   `[24*(4542) ]/[(6+73)0]`  the last one is supposed to be closer to the line. Please simlify equation and show work and...

simplify the following

`(36*3 - 2) 3 -: 3 - 2`

`(2/5)3 (2/5)-2`

`[24*(4542) ]/[(6+73)0]`

the last one is supposed to be closer to the line. Please simlify equation and show work and formulas used

lemjay | Certified Educator

In simplifying arithmetic expression, follow the order of operations which is:

I: Do the operations inside the parenthesis,

II: Multiply and/or divide whichever comes first starting from left  going to right, and

III: Do the addition and/or subtraction working from left to right too.

(1) Simplify `(36*3-2)3-:3-2`

First, simplify inside the parenthesis. Inside, there are two operations, multiplication and subtraction. The order of operation for this is multiply, then subtract.

`(36*3-2)3-:3-2 = (108 - 2)3 -:3-2 = 106*3-:3-2`

Next,do the multiplication since it comes first.

`= 318 -: 3 - 2`

Divide, then subtract.

`= 106-2 = 104`

(2) `(2/5)3(2/5)-2`

Multiply first. Note that when multiplying a fraction with a whole number, multiply only the numerator and the whole number. The product becomes the new numerator and the denominator is still the same.

`(2/5)(3)(2/5)-2 = 6/5(2/5)-2`

In multiplying fractions, multiply the two numerators. Also, multiply the two denominators. The products become the new numerator and denominator respectively.

`=12/25 - 2`

Before subtracting, determine the LCD which is 25. So, express 2 as a fraction, 25 as its denominator.

`= 12/25-50/25 = -38/25 = -1 13/25`

The difference has a negative sign as per rule of subtraction which is subtracting a large number from a smaller one results to a negative number.

(3) `[24*(4542)] /[ (6+73)0]`

Do the indicated operations at the numerator and also at the denominator.

`=109008/[(79)0] = 109008/0`

Note that in fraction, the denominator should not be equal to zero. A zero denominator is an invalid expression.

Answer: `[24(4542)]/(6+73)0` results to undefined value or invalid expression.