Simplify each exponential expression in Exercises 23–64. x−5⋅$$x10x^{-5}$$\cdot $$x^{10}$$

Ch. P - Fundamental Concepts of Algebra

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

Problem 29

Chapter 1, Problem 29

Simplify each exponential expression in Exercises 23–64. $x^{- 5} \cdot x^{10}$

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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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Key Concepts

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

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).

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.

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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