Simplify each expression. See Example 1. (3y⁴)(-6y³)

Verified step by step guidance

1. Identify the expression to simplify: \( (3y^{4})(-6y^{3}) \).
2. Apply the associative property to group the coefficients and the variables separately: \( (3 \times -6)(y^{4} \times y^{3}) \).
3. Multiply the coefficients: \( 3 \times -6 = -18 \).
4. Use the product of powers property for the variables: \( y^{4} \times y^{3} = y^{4+3} = y^{7} \).
5. Combine the results to write the simplified expression: \( -18y^{7} \).

Key Concepts

Product of Powers Property

When multiplying expressions with the same base, add the exponents. For example, y^4 * y^3 equals y^(4+3) = y^7. This property simplifies expressions involving powers of the same variable.

Multiplying Coefficients

Multiply the numerical coefficients separately from the variables. In (3y^4)(-6y^3), multiply 3 and -6 to get -18. This step simplifies the numerical part of the expression.

Simplifying Algebraic Expressions

Combine like terms and apply exponent rules to rewrite expressions in simplest form. This involves careful handling of signs, coefficients, and exponents to produce a clear, simplified result.