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

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 12

Chapter 1, Problem 12

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

Verified step by step guidance

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: \( -18y^{7} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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