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

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 12

1장, 문제 12

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

검증된 단계별 안내

Identify the expression to simplify: \( (3y^{4})(-6y^{3}) \).

Apply the associative property to group the coefficients and the variables separately: \( (3 \times -6)(y^{4} \times y^{3}) \).

Multiply the coefficients: \( 3 \times -6 = -18 \).

Use the product of powers property for the variables: \( y^{4} \times y^{3} = y^{4+3} = y^{7} \).

Combine the results to write the simplified expression: \( -18y^{7} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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, 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.