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Question Video: Using Order of Operations to Evaluate Numerical Expressions Involving Exponents Mathematics • 6th Grade

Calculate (5 − 3)³ − 7 + (4 × 6).

02:09

Video Transcript

Calculate five minus three cubed minus seven plus four multiplied by six.

We begin by noticing that the calculations five minus three and four multiplied by six are inside parentheses or brackets. In order to calculate the expression, we recall the order of operations. One way of doing this is using the acronym PEMDAS. The letters stand for parentheses, exponents, multiplication, division, addition, and subtraction. It is worth noting that it is also common to write this as four steps, where we group multiplication and division as well as addition and subtraction.

Returning to our question, we begin by calculating the expressions in the parentheses. Five minus three equals two, and four multiplied by six equals 24. So our expression simplifies to two cubed minus seven plus 24. Next, we notice that the first term contains an exponent. Since two cubed is equal to eight, we now have eight minus seven plus 24.

We are now left with two operations, addition and subtraction. Whilst addition comes first in the acronym, we can perform these in either order. And convention dictates we work from left to right. Eight minus seven equals one, and adding 24 to this gives us 25. Five minus three cubed minus seven plus four multiplied by six is therefore equal to 25.

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