What is the sum of 6^3/5+5^1/7?
Enter your answer as a mixed number in lowest terms, like this: 4 2/5
I hope you mean
6 3/5 + 5 1/7
= 33/5 + 36/7
= 33*7/35 + 36*5/35
= 231/35 + 180/35
= 411/35
= 11 26/35
If you meant what you wrote, then
6^3/5 + 5^1/7
= 216/5 + 5/7
= 1537/35
= 43 22/35
Thank you
6 3/5 + 5 1/7
To find the sum of 6^(3/5) and 5^(1/7), we first need to evaluate each exponent separately.
Let's start with 6^(3/5):
To calculate it, we raise 6 to the power of the fraction 3/5.
The general formula for calculating a fraction exponent is: a^(m/n) = n√(a^m).
Applying this formula to 6^(3/5), we get:
6^(3/5) = 5√(6^3).
Evaluating the cube of 6:
6^3 = 6 * 6 * 6 = 216.
Now, let's find the fifth root of 216:
5√(216) ≈ 2.828.
So, 6^(3/5) is approximately equal to 2.828.
Next, let's evaluate 5^(1/7):
Using the same formula, we have:
5^(1/7) = 7√(5^1).
Since any number raised to the power of 1 is the number itself, we have:
7√(5^1) = 7√5.
Now, we need to simplify the expression as much as possible:
The expression 7√5 is not a perfect root, so we cannot simplify it further.
Finally, we sum the two values we obtained:
2.828 + 7√5.
Since the instructions ask for the answer in the form of a mixed number, we need to convert 2.828 into a mixed number.
To do this, we first find the whole number part of 2.828, which is 2.
The decimal part, 0.828, can be expressed as a fraction by putting the decimal part over the appropriate power of 10. The fraction is 828/1000.
Reducing this fraction to lowest terms, we divide both the numerator and the denominator by their greatest common divisor, which is 4:
828/1000 = (828 ÷ 4) / (1000 ÷ 4) = 207/250.
Therefore, the mixed number form of 2.828 is 2 207/250.
So, the sum 6^(3/5) + 5^(1/7) is approximately equal to 2 207/250.