The correct expressions are as follows:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Further explanation
Let's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem!
[tex]\texttt{ }[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}[/tex]
[tex]\texttt{ }[/tex]
From the results above, it can be concluded that the correct statements are:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Coefficient of A Square Root : https://brainly.com/question/11337634
- The Order of Operations : https://brainly.com/question/10821615
- Write 100,000 Using Exponents : https://brainly.com/question/2032116
Answer details
Grade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
