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Video: Computing Numerical Expressions Using Laws of Exponents

Kathryn Kingham

What is the value of 3 × 3² − 6 ÷ 3 × 7 + 8?


Video Transcript

What is the value of three times three squared minus six divided by three times seven plus eight?

To solve this question, we’ll need to use the order of operations. This is the order that we follow when evaluating expressions or equations. We start here. Our expression does not have any form of grouping or parentheses, which means we can move on to the exponents step. This expression has one exponent, three squared.

We will go ahead and evaluate what three squared is. Three squared is nine. Since there are no other exponents in the expression, that step is finished. Now we just copy down the expression exactly how it was written above with the exception of adding in a nine for three squared. The next thing that comes up in order of operations is multiply and divide. When we do multiplication and division in expressions or equations, we multiply and divide from left to right. This means that sometimes we will divide before we multiply. I’ll show you.

This expression has three instances of multiplication or division. And we’re gonna solve them by moving from left to right. First up, three times nine. That equals twenty-seven. Copy down the equation. Move from left to right, looking for multiplication or division, we find division: six divided by three. That equals two. Bring down the rest of the expression. Look for multiplication or division. We find two times seven. Two times seven equals fourteen. There are no more multiplication or division operations. Now we want to add and subtract, moving from left to right. Twenty-seven minus fourteen is thirteen. Bring down the expression. Thirteen plus eight equals twenty-one. We finished the order of operations. To answer the question we were asked, what is the value of that expression, the value is twenty-one.