Question Video: Simplifying Algebraic Expressions Using Laws of Exponents Mathematics • 9th Grade

Simplify (6𝑥³ − 3𝑥³) ÷ 3𝑥².


Video Transcript

Simplify six 𝑥 cubed minus three 𝑥 cubed divided by three 𝑥 squared.

Inside our parentheses here, we have two like terms, two terms that have the same variable taken to the same power. This means that we can simply subtract. Six 𝑥 cubed minus three 𝑥 cubed equals three 𝑥 cubed. In order to divide this value by three 𝑥 squared though, we’ll need to change a few things. We can keep our first term, bring down the three 𝑥 cubed. But we need to change our division to multiplication and take the reciprocal of three 𝑥 squared, which would be one over three 𝑥 squared. Three 𝑥 cubed times one equals three 𝑥 cubed. We can add a denominator of one and then say one times three 𝑥 squared equals three 𝑥 squared.

From here, we notice that three over three be equal to one, they cancel each other out. And we’re left with 𝑥 cubed over 𝑥 squared. If we drew out 𝑥 cubed and 𝑥 squared, it would look like this. 𝑥 over 𝑥 equals one; they cancel out. 𝑥 over 𝑥 equals one, and those cancel out leaving us with 𝑥. But we don’t have to draw them out. What we can say when we’re dividing with exponents is that 𝑥 to the third power divided by 𝑥 squared equals 𝑥 to the three minus two power. We took the power from the numerator and then you subtract the power of the denominator from the power of the numerator.

Both options produce the solution 𝑥 to the first power or 𝑥.

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