1Cademy - Multiplying $$(\frac{2}{3}r^5s)(12r^6s^7)$$

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Multiplying Monomials

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Multiplying $(\frac{2}{3}r^5s)(12r^6s^7)$

Multiply the two multi-variable monomials $(\frac{2}{3}r^5s)(12r^6s^7)$ .

Step 1 — Rearrange using the Commutative Property. Group the numerical coefficients together and group the corresponding variable bases:

$\frac{2}{3} \cdot 12 \cdot r^5 \cdot r^6 \cdot s \cdot s^7$

Step 2 — Multiply coefficients and apply the Product Property. The product of the numerical parts is $\frac{2}{3} \cdot 12 = 8$ . Adding the exponents for each variable gives $r^{5+6} = r^{11}$ and $s^{1+7} = s^8$ .

The final result is $8r^{11}s^8$ .

Updated 2026-05-25

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

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