To simplify this expression, we can use the property of exponents that states (a^m)^n = a^(m*n).
Using this property, we can write:
(13)^(1/5) . (17)^(1/5) = (13.17)^(1/5)
We can simplify this further by finding the fifth root of 13.17. We can do this using a calculator or by hand using estimation and trial and error.
One possible approximation is to note that 3^5 = 243 and 4^5 = 1024. Since 13 is between 3^2 and 4^2, we can estimate that the fifth root of 13 is between 3 and 4. Similarly, since 17 is between 4^2 and 5^2, we can estimate that the fifth root of 17 is between 4 and 5.
Using these estimations, we can conclude that:
(13)^(1/5) . (17)^(1/5) ≈ (3.5)^(1/5) ≈ 1.699
Therefore, the simplified expression is approximately 1.699.
Answers & Comments
To simplify this expression, we can use the property of exponents that states (a^m)^n = a^(m*n).
Using this property, we can write:
(13)^(1/5) . (17)^(1/5) = (13.17)^(1/5)
We can simplify this further by finding the fifth root of 13.17. We can do this using a calculator or by hand using estimation and trial and error.
One possible approximation is to note that 3^5 = 243 and 4^5 = 1024. Since 13 is between 3^2 and 4^2, we can estimate that the fifth root of 13 is between 3 and 4. Similarly, since 17 is between 4^2 and 5^2, we can estimate that the fifth root of 17 is between 4 and 5.
Using these estimations, we can conclude that:
(13)^(1/5) . (17)^(1/5) ≈ (3.5)^(1/5) ≈ 1.699
Therefore, the simplified expression is approximately 1.699.