Question

How do you simplify `3^ { 4} - 24\div 4\cdot 4- \frac { 54} { 6}`?

Answer 1

`3^4-24-:4*4-54/6=color(blue)48`

Explanation:

Simplify:

`3^4-24-:4*4-54/6`

This expression can be simplified by using the order of operations, which is represented by the acronym PEMDAS , which means:

Parentheses (brackets)

Exponents (powers)

Multiplication and Division from left to right because they are equal in rank.

Addition and Subtraction from left to right because they are equal in rank.

We don't have parentheses or brackets, but we do have an exponent.

Simplify the exponent `3^4` to `81`.

`color(red)81-24-:4*4-54/6`

Next simplify `24-:4` to `6`.

`color(red)81-color(blue)6*4-54/6`

Simplify `6*4` to `24`.

`color(red)81-color(purple)24-54/6`

Simplify `54/6` to `9`.

`color(red)81-color(purple)24-color(green)9`

Simplify.

`48`

Answer 2

`3^4 -24 div 4 xx 4 -54/6`

#=48

Explanation:

In any calculation with different operations count the number of TERMS first. They are separated by `+ and -` signs,

Simplify each term to a single value and these are added or subtracted in the last step.
Within each term the order is:

• brackets
• powers and roots
• multiply and divide

You can work in different terms in the same line of working.

`" "color(blue)(3^4) -color(red)(24/cancel4 xx cancel4)color(green)( -54/6)" "larr` there are 3 terms

`=color(blue)(81) " "color(red)(-24)" "color(green)( -9)`

`=57-9`

`=48`