Simplify each expression. (-8t3)(2t6)(-5t4)

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 18

1장, 문제 18

Simplify each expression. (-8t³)(2t⁶)(-5t⁴)

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Identify the coefficients (numerical parts) and the variable parts separately in the expression \((-8t^{3})(2t^{6})(-5t^{4})\).

Multiply the coefficients together: \(-8 \times 2 \times -5\).

Apply the product rule for exponents to the variable parts: when multiplying like bases, add the exponents. So, add the exponents of \(t\): \(3 + 6 + 4\).

Combine the results from the coefficient multiplication and the variable exponent addition to write the simplified expression in the form \(a t^{b}\), where \(a\) is the product of coefficients and \(b\) is the sum of exponents.

Write the final simplified expression, ensuring the correct sign and exponent are included.

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주요 개념

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

Multiplication of Coefficients

When multiplying expressions, multiply the numerical coefficients (constants) separately from the variables. For example, in (-8)(2)(-5), multiply the numbers to get the new coefficient before combining the variable parts.

Product of Powers Property

When multiplying variables with the same base, add their exponents. For instance, t³ × t⁶ × t⁴ equals t^(3+6+4) = t¹³. This property simplifies expressions with powers efficiently.

Handling Negative Signs in Multiplication

Multiplying negative numbers follows sign rules: the product of two negatives is positive, and the product of a positive and a negative is negative. Keep track of signs to determine the final sign of the product.