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
![**Simplify the Expression**
The expression to simplify is:
\[ c^{\frac{3}{4}} \cdot c^{\frac{3}{7}} \]
To simplify expressions like this, use the property of exponents which states that when multiplying like bases, you add the exponents:
\[ c^{\frac{3}{4} + \frac{3}{7}} \]
To add the exponents \(\frac{3}{4}\) and \(\frac{3}{7}\), find a common denominator:
1. The least common denominator of 4 and 7 is 28.
2. Convert the fractions:
- \(\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}\)
- \(\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}\)
3. Add the fractions:
- \(\frac{21}{28} + \frac{12}{28} = \frac{33}{28}\)
4. The simplified expression is:
- \( c^{\frac{33}{28}} \)
Thus, the simplified form of the expression is \( c^{\frac{33}{28}} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F322e30c4-04c1-4495-b21b-e5cf49b8347a%2F560cfcb2-a29a-483f-82d5-b93b842eef5a%2Fdo80qn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Simplify the Expression**
The expression to simplify is:
\[ c^{\frac{3}{4}} \cdot c^{\frac{3}{7}} \]
To simplify expressions like this, use the property of exponents which states that when multiplying like bases, you add the exponents:
\[ c^{\frac{3}{4} + \frac{3}{7}} \]
To add the exponents \(\frac{3}{4}\) and \(\frac{3}{7}\), find a common denominator:
1. The least common denominator of 4 and 7 is 28.
2. Convert the fractions:
- \(\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}\)
- \(\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}\)
3. Add the fractions:
- \(\frac{21}{28} + \frac{12}{28} = \frac{33}{28}\)
4. The simplified expression is:
- \( c^{\frac{33}{28}} \)
Thus, the simplified form of the expression is \( c^{\frac{33}{28}} \).
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