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Factor using the formula for the sum or difference of two cubes.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 58
Simplify each exponential expression in Exercises 23–64.
Guida verificata passo dopo passo1
Start by writing the expression clearly: \(\frac{10x^{4} y^{9}}{30x^{12} y^{-3}}\).
Simplify the coefficients (numerical parts) by dividing 10 by 30, which gives \(\frac{10}{30}\).
Apply the quotient rule for exponents to the variables with the same base: for \(x\), subtract the exponents in the denominator from those in the numerator: \(x^{4 - 12}\); for \(y\), do the same: \(y^{9 - (-3)}\).
Rewrite the expression with the simplified coefficients and the new exponents: \(\frac{10}{30} x^{4 - 12} y^{9 - (-3)}\).
Simplify the numerical fraction and the exponents to get the final simplified expression.
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Laws of Exponents
The laws of exponents govern how to simplify expressions involving powers. Key rules include dividing powers with the same base by subtracting exponents, multiplying powers by adding exponents, and handling negative exponents by rewriting them as reciprocals. These rules allow simplification of expressions like the given one.
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Rational Exponents
Simplifying Algebraic Fractions
Simplifying algebraic fractions involves reducing coefficients and variables separately. Coefficients are simplified by dividing their numerical values, while variables with exponents are simplified using exponent rules. This process helps to rewrite the expression in its simplest form.
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05:07Simplifying Algebraic Expressions
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example, x^(-n) equals 1/x^n. Understanding this concept is essential to simplify terms like y^(-3) in the denominator by moving them to the numerator with a positive exponent.
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6:37Zero and Negative Rules
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