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

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 29

1장, 문제 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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주요 개념

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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).

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.

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