Video: Using Order of Operations to Evaluate Numerical Expressions Involving Exponents by Identifying the Greatest Common Factor

Determine the value of |(((22)² × 25) − (4 × (22)²))/(−7 × (22)²)| by identifying the greatest common factor.

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Video Transcript

Determine the value of the absolute value of 22 squared times 25 minus four times 22 squared all over negative seven times 22 squared by identifying the greatest common factor.

We have this expression that has an absolute value. And we want to determine exactly what value this expression represents. However, our instructions have said to find this value by identifying the greatest common factor. By identifying the greatest common factor, we can first simplify our expression and secondly solve for the value.

A greatest common factor will be a factor that is shared in the numerator and the denominator. Looking carefully here, we see that we have 22 squared occurring twice in the numerator and once in the denominator. And this is where we need to be very careful. Notice in the denominator we are only doing multiplication. However, in the numerator, we have some subtraction. 22 squared times 25 is a term together, and four times 22 squared is another term. And that means we’ll need to do some rearranging in the numerator.

Since both terms in the numerator have a factor of 22 squared, we can undistribute that 22 squared and rewrite the numerator as 22 squared times 25 minus four. This is because both 25 and four were being multiplied by 22 squared. Once we do this, we can bring down everything else from our expression. Our denominator is negative seven times 22 squared. If we wanted to rearrange this multiplication, we could write that as 22 squared times negative seven.

And at this point, we see that we have a common factor in the numerator and the denominator. And that is the factor of 22 squared. 22 squared over 22 squared equals one, which means we can simplify our expression to be the absolute value of 25 minus four over negative seven. 25 minus four is 21. Then we have the absolute value of 21 over negative seven.

At this point, we’re ready to start solving. 21 divided by negative seven is negative three. And the absolute value of negative three is positive three. And that means the value of our initial expression is three.

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