Simplify each expression. x y ⋅ 3 x 2 xy\cdot3x^2

For this problem, we want to simplify the expression x times y times three times x squared. And we're going to use the product rule. Now first, it might not look like we can apply the product rule since our term x times y and three times x squared don't have the same base. But first, we're going to break apart these terms to see that we do have certain terms within our terms that do have a common base. So let's first look at this by rewriting it as x times y times three times x squared. Now, do any of these terms have a common base? Yes. Our x and our x squared. So we can go ahead and combine those two terms using our product rule. And doing that, we get x to the one plus two power, which is three, times y times three. And this is our expression written in its simplest form.

6. Exponents and Polynomials

The Product Rule

Beginning Algebra

6. Exponents and Polynomials

The Product Rule

Struggling with Beginning Algebra?

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Multiple Choice

Simplify each expression.
$x y times 3 x squared$

$3x^3y$

$3xy^3$

$3x^3$

$3xy^2$

Verified step by step guidance

Recall the Product Rule for Exponents, which states that when multiplying two expressions with the same base, you add their exponents: $a^{m} \times a^{n} = a^{m+n}$.

Identify the base and the exponents in the given problem. Make sure the bases are the same before applying the rule.

Add the exponents together while keeping the base the same, according to the Product Rule.

Rewrite the expression with the base and the new exponent sum: $a^{m+n}$.

Simplify the expression if possible, but do not calculate the numerical value unless asked.

3:48m

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Struggling with Beginning Algebra?

Simplify each expression.xy⋅3x2xy\cdot3x^2

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Simplify each expression.
$x y times 3 x squared$