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

Verified step by step guidance

1. Identify the expression to simplify: \((3y^4)(-6y^3)\).
2. Multiply the coefficients (numerical parts) together: \$3 \times (-6)$.
3. Apply the product rule for exponents with the same base: \(y^4 \times y^3 = y^{4+3}\).
4. Combine the results from the coefficient multiplication and the exponent multiplication to write the simplified expression.
5. Write the final simplified expression in the form \(ay^b\), where \(a\) is the product of the coefficients and \(b\) is the sum of the exponents.

Key Concepts

Multiplication of Coefficients

When multiplying expressions, multiply the numerical coefficients (numbers) separately from the variables. For example, in (3y^4)(-6y^3), multiply 3 and -6 to get -18.

Product of Powers Property

When multiplying variables with the same base, add their exponents. For instance, y^4 * y^3 equals y^(4+3) = y^7.

Simplifying Algebraic Expressions

Simplifying involves combining like terms and applying arithmetic operations to write the expression in its simplest form. Here, after multiplying coefficients and applying exponent rules, write the final simplified product.