Simplify each expression. See Example 1.(5x²y) (-3x³y⁴)

Verified step by step guidance

1. Identify the coefficients and multiply them: \(5 \times (-3)\).
2. Multiply the powers of \(x\) by adding the exponents: \(x^2 \times x^3 = x^{2+3}\).
3. Multiply the powers of \(y\) by adding the exponents: \(y^1 \times y^4 = y^{1+4}\).
4. Combine the results from the previous steps to form the simplified expression.
5. Ensure all like terms are combined and the expression is fully simplified.

Key Concepts

Multiplication of Monomials

Multiplying monomials involves multiplying their coefficients and adding the exponents of like bases. For example, when multiplying (5x²y) and (-3x³y⁴), you multiply 5 and -3 to get -15, and for the variable x, you add the exponents 2 and 3 to get x⁵. Similarly, for y, you add the exponents 1 and 4 to get y⁵.

Exponent Rules

Exponent rules are essential for simplifying expressions involving powers. The key rules include the product of powers rule, which states that when multiplying like bases, you add the exponents. This is crucial in the given expression, as it allows for the correct combination of the x and y terms when simplifying.

Combining Like Terms

Combining like terms is the process of simplifying expressions by merging terms that have the same variable raised to the same power. In the context of the expression (5x²y)(-3x³y⁴), after applying multiplication and exponent rules, the resulting terms can be combined to form a single simplified expression, ensuring clarity and conciseness.