Product of Monomials
Monomials are algebraic expressions that consist of a single term. In this case, we are given three monomials: S^2, -Sm, and S^3n. To find the product of these monomials, we need to multiply them together.
Step 1: Multiply the coefficients
- The coefficient of S^2 is 1 because it is understood to be 1*S^2.
- The coefficient of -Sm is -1 because it is understood to be -1*Sm.
- The coefficient of S^3n is 1 because it is understood to be 1*S^3n.
Step 2: Multiply the variables
- The variable in S^2 is S raised to the power of 2.
- The variable in -Sm is S raised to the power of 1 and m.
- The variable in S^3n is S raised to the power of 3 and n.
Step 3: Multiply the coefficients and variables together
- Multiplying the coefficients 1 * (-1) * 1 gives us -1.
- Multiplying the variables S^2 * S * S^3 gives us S^6.
- Multiplying the variables m and n together gives us mn.
Step 4: Combine the results
- Putting it all together, the product of S^2, -Sm, and S^3n is -S^6mn.