Question

Simplify each expression. $$x^{7} x^{3} x^{-5}$$

   Simplify each expression.
$$x^{7} x^{3} x^{-5}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 2, Problem 123

Instant Answer

Solved by Expert Michael Jacobsen

07/08/2020

Step 1

According to the laws of exponents, when we multiply expressions with the same base, we add the exponents. Show more…

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Simplify each expression. $$x^{7} x^{3} x^{-5}$$

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Key Concepts

Properties of Exponents

The laws of exponents provide rules for manipulating expressions that involve powers. One essential property is the product of powers rule, which states that when multiplying terms with the same base, you can add the exponents together. This rule simplifies the process of combining exponential expressions and is fundamental to algebraic manipulation.

Negative Exponents

A negative exponent indicates that the base is located in the denominator rather than the numerator when expressed in fractional form. Working with negative exponents involves understanding that a term raised to a negative power represents the reciprocal of the term raised to the corresponding positive power, which is a critical concept in simplifying expressions with exponents.

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