Simplify each expression. See Example 1. (-4x⁵) (4x²)

검증된 단계별 안내

Identify the properties of exponents and multiplication that apply. When multiplying terms with the same base, you multiply the coefficients and add the exponents of the variables.

Multiply the coefficients: here, multiply -4 and 4, which gives \(-4 \times 4\).

Apply the product rule for exponents to the variable part: since the bases are the same (both are \(x\)), add the exponents \(5\) and \(2\) using \(x^{5} \times x^{2} = x^{5+2}\).

Combine the results from the coefficient multiplication and the exponent addition to write the simplified expression as a product of the new coefficient and the variable with the summed exponent.

Write the final simplified expression in the form \(ax^{b}\), where \(a\) is the product of the coefficients and \(b\) is the sum of the exponents.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Product of Powers Property

When multiplying expressions with the same base, add the exponents. For example, x^a * x^b = x^(a+b). This property simplifies expressions involving powers of variables.

Multiplication of Coefficients

Multiply the numerical coefficients separately from the variables. For instance, in (-4x⁵)(4x²), multiply -4 and 4 to get -16 before combining the variable parts.

Simplifying Algebraic Expressions

Combine like terms and apply arithmetic operations to rewrite expressions in simpler forms. This involves using exponent rules and basic multiplication to reduce complexity.