1Cademy - Multiplying $$(5y^7)(-7y^4)$$

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Multiplying Monomials

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Multiplying $(5y^7)(-7y^4)$

Multiply the two single-variable monomials $(5y^7)(-7y^4)$ .

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

$5 \cdot (-7) \cdot y^7 \cdot y^4$

Step 2 — Multiply coefficients and apply the Product Property. The product of the coefficients is $5 \cdot (-7) = -35$ . Adding the exponents of the shared base $y$ gives $y^{7+4} = y^{11}$ .

The final product is $-35y^{11}$ .

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

Algebra

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A quality assurance tester is verifying a calculation script that simplifies the monomial product $(5y^7)(-7y^4)$ . According to the procedural rules of algebra, the script should correctly multiply the coefficients (5 and -7) to get -35, and multiply the exponents (7 and 4) to get 28, resulting in a final output of $-35y^{28}$ .

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