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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 29
Chapter 1, Problem 29

Simplify each exponential expression: (−5x3y2)(−2x−11y−2)(-5x^3y^2)(-2x^{-11}y^{-2})

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1
Identify the expression to simplify: \((-5x^{3}y^{2})(-2x^{-11}y^{-2})\).
Multiply the coefficients (numbers) together: \(-5 \times -2\).
Apply the product rule for exponents to the \(x\) terms: \(x^{3} \times x^{-11} = x^{3 + (-11)}\).
Apply the product rule for exponents to the \(y\) terms: \(y^{2} \times y^{-2} = y^{2 + (-2)}\).
Combine the results from the coefficient multiplication and the simplified variables to write the final simplified expression.

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Key Concepts

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

Laws of Exponents

The laws of exponents govern how to simplify expressions involving powers. Key rules include multiplying powers with the same base by adding their exponents, and handling negative exponents by rewriting them as reciprocals. These rules allow simplification of expressions like x^a * x^b = x^(a+b).
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Multiplication of Algebraic Expressions

When multiplying algebraic expressions, multiply the coefficients (numerical parts) separately from the variables. For variables with exponents, apply the laws of exponents. This process helps combine terms systematically to simplify the overall expression.
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Handling Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the positive exponent, e.g., x^(-n) = 1/x^n. Understanding this allows rewriting terms with negative exponents into fractions or adjusting exponents during multiplication to simplify expressions correctly.
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