Video: Evaluating Numerical Expressions with Integer Exponents Using Laws of Exponents

Find the value of (−3)³ × (3²)³.


Video Transcript

Find the value of negative three cubed times three squared cubed.

Following the order of operations, we need to work inside the parentheses first. So inside the first parenthesis, we have negative three. So there’s nothing to do. It’s just a negative three. Now inside the second one, we have three squared. And three squared is equal to nine. So we have negative three cubed times nine cubed. So these exponents are powers. We’re raising these numbers to a power. Or, we can think of it as negative three cubed means we’re multiplying negative three to itself three times. And we’re multiplying nine to itself three times. We have negative three times negative three times negative three times nine times nine times nine.

Now we could go ahead and multiply all these numbers together on our calculator. Or, if we want to split it up into pieces, negative three times negative three times negative three is negative 27. And nine times nine times nine is 729. Now multiplying these numbers together, we get negative 19683. So again, we could’ve multiplied all of the numbers together here or multiply them in sections. It wouldn’t have mattered.

So once again, our final answer is negative 19683.

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