How do you multiply x to the 1/3 power times x to the 3/7 power?

To multiply two expressions with the same base, you simply add their exponents. In this case, you have x raised to the 1/3 power and x raised to the 3/7 power. So, the calculation looks like this:

x^1/3 * x^3/7 = x^{(1/3 + 3/7)}

Now, we need to add the fractions 1/3 and 3/7. To do this, we first find a common denominator, which in this case is 21. We convert both fractions:

• 1/3 = 7/21
• 3/7 = 9/21

Now we can add them together:

7/21 + 9/21 = 16/21

Therefore, the final result of multiplying x^1/3 and x^3/7 is:

x^16/21

So, x to the 1/3 power times x to the 3/7 power equals x to the 16/21 power.