1Cademy - Multiplying $$\left(\frac{5}{6}x^3y\right)(12xy^2)$$

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Monomial

Example

Multiplying $\left(\frac{5}{6}x^3y\right)(12xy^2)$

Multiply the two monomials $\left(\frac{5}{6}x^3y\right)(12xy^2)$ , which involve a fractional coefficient and two different variables.

Step 1 — Rearrange using the Commutative Property. Group the numerical coefficients together and the powers of each variable together:

$\frac{5}{6} \cdot 12 \cdot x^3 \cdot x \cdot y \cdot y^2$

Step 2 — Multiply the coefficients. Compute $\frac{5}{6} \cdot 12 = 10$ .

Step 3 — Apply the Product Property to each variable base. For $x$ : recall that $x$ written without an exponent has an implicit exponent of $1$ , so $x^3 \cdot x = x^{3+1} = x^4$ . For $y$ : similarly, $y \cdot y^2 = y^{1+2} = y^3$ .

The result is $10x^4y^3$ .

This example extends the monomial multiplication procedure to expressions with multiple variables and a fractional coefficient. The Product Property is applied independently to each variable base, and the fractional coefficient is multiplied with the integer coefficient using standard fraction arithmetic.

Updated 2026-04-21

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OpenStax Elementary Algebra

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