Textbook Question
Write each improper fraction as a mixed number. 16/9
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Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 1, Problem 19
Simplify each expression. See Example 1. (5x2y)(-3x3y4)
Verified step by step guidance1
Identify the expression to simplify: \((5x^{2}y)(-3x^{3}y^{4})\).
Apply the multiplication property of exponents by multiplying the coefficients (numbers) together: multiply 5 and -3.
Use the product rule for exponents on the variable \(x\): when multiplying like bases, add the exponents, so \(x^{2} \times x^{3} = x^{2+3}\).
Use the product rule for exponents on the variable \(y\): multiply \(y\) (which is \(y^{1}\)) by \(y^{4}\), so \(y^{1} \times y^{4} = y^{1+4}\).
Combine the results from the coefficients and variables to write the simplified expression as a product of the new coefficient and the variables with their summed exponents.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Multiplication of Monomials
When multiplying monomials, multiply their coefficients (numerical parts) and then multiply variables by adding their exponents if the bases are the same. For example, (5x²)(-3x³) equals -15x⁵.
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Finding Zeros & Their Multiplicity
Laws of Exponents
The laws of exponents state that when multiplying like bases, add their exponents. For instance, x² * x³ = x^(2+3) = x⁵. This rule applies to all variables with exponents in the expression.
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04:06Rational Exponents
Combining Variables with Different Exponents
When variables with the same base but different exponents are multiplied, add the exponents to simplify. For example, y * y⁴ = y^(1+4) = y⁵. This helps in simplifying expressions involving multiple variables.
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7:39Introduction to Exponent Rules
Related Practice
Textbook Question
Write each root using exponents and evaluate. ∜-256
Textbook Question
Write each improper fraction as a mixed number. 77/12
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Textbook Question
Write each root using exponents and evaluate. ⁵√32
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Textbook Question
Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. (3/8)x5-(1/x2)+9
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Textbook Question
Factor out the greatest common factor from each polynomial. See Example 1.