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12. Explain what a rational exponent, such as 5 means. Use this explanation to evaluate 92.

12. Explain what a rational exponent, such as 5 means. Use this explanation to evaluate 92.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 12** *Explain what a rational exponent, such as \( \frac{5}{2} \) means. Use this explanation to evaluate \( 9^{\frac{5}{2}} \).* *Type your response here or upload a picture here* --- **Explanation for Educational Website:** A rational exponent is an exponent that is expressed as a fraction. For example, \( \frac{5}{2} \) is a rational exponent. The general form of a rational exponent is \( \frac{m}{n} \) where both \( m \) and \( n \) are integers. To understand what a rational exponent represents, you can break it down into two parts: 1. The denominator (\( n \)) represents the root. 2. The numerator (\( m \)) represents the power to which the result is raised. In this case, for \( \frac{5}{2} \): - The denominator 2 means taking the square root. - The numerator 5 means raising the result to the 5th power. Using this explanation, let's evaluate \( 9^{\frac{5}{2}} \): 1. First, take the square root of 9: \( \sqrt{9} = 3 \). 2. Then, raise the result to the 5th power: \( 3^5 = 243 \). Therefore, \( 9^{\frac{5}{2}} = 243 \). For further practice, you can follow this same process to evaluate other expressions with rational exponents.
Transcribed Image Text:**Question 12** *Explain what a rational exponent, such as \( \frac{5}{2} \) means. Use this explanation to evaluate \( 9^{\frac{5}{2}} \).* *Type your response here or upload a picture here* --- **Explanation for Educational Website:** A rational exponent is an exponent that is expressed as a fraction. For example, \( \frac{5}{2} \) is a rational exponent. The general form of a rational exponent is \( \frac{m}{n} \) where both \( m \) and \( n \) are integers. To understand what a rational exponent represents, you can break it down into two parts: 1. The denominator (\( n \)) represents the root. 2. The numerator (\( m \)) represents the power to which the result is raised. In this case, for \( \frac{5}{2} \): - The denominator 2 means taking the square root. - The numerator 5 means raising the result to the 5th power. Using this explanation, let's evaluate \( 9^{\frac{5}{2}} \): 1. First, take the square root of 9: \( \sqrt{9} = 3 \). 2. Then, raise the result to the 5th power: \( 3^5 = 243 \). Therefore, \( 9^{\frac{5}{2}} = 243 \). For further practice, you can follow this same process to evaluate other expressions with rational exponents.
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