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Simplify each exponential expression:
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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 29
Simplify each exponential expression in Exercises 23–64.
Guida verificata passo dopo passo1
Recall the property of exponents that states when multiplying two expressions with the same base, you add their exponents: \(a^m \cdot a^n = a^{m+n}\).
Identify the base and the exponents in the expression \(x^{-5} \cdot x^{10}\). Here, the base is \(x\), and the exponents are \(-5\) and \(10\) respectively.
Apply the exponent addition rule by adding the exponents: \(-5 + 10\).
Write the expression with the new exponent: \(x^{-5 + 10} = x^{5}\).
The simplified form of the expression is \(x^{5}\).
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Laws of Exponents
The laws of exponents provide rules for simplifying expressions involving powers. For multiplication of like bases, add the exponents (e.g., x^a * x^b = x^(a+b)). This rule is essential for combining terms like x^(-5) and x^(10).
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04:06
Rational Exponents
Negative Exponents
A negative exponent indicates the reciprocal of the base raised to the positive exponent (x^(-n) = 1/x^n). Understanding this helps in simplifying expressions where exponents are negative, converting them into fractions if needed.
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6:37Zero and Negative Rules
Simplification of Exponential Expressions
Simplification involves applying exponent rules to rewrite expressions in a simpler or more standard form. This includes combining like terms, reducing powers, and expressing answers without negative exponents when possible.
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6:39Simplifying Exponential Expressions
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