How do you multiply x to the one-third power by x to the three-sevenths power?

To multiply expressions with the same base, you can simply add the exponents. In this case, we need to multiply x^{1/3} by x^{3/7}.

The rule for multiplying exponents is as follows:

• If you have a^m multiplied by a^n, the result is a^{m+n}.

So, let’s add the exponents:

Start by rewriting the expression:

x^{1/3} imes x^{3/7}

Now, add the exponents:

1/3 + 3/7

To add these fractions, we need a common denominator. The least common multiple of 3 and 7 is 21.

Convert 1/3 and 3/7 to have 21 as the denominator:

• 1/3 = 7/21 (multiply the numerator and the denominator by 7)
• 3/7 = 9/21 (multiply the numerator and the denominator by 3)

Now we can add the fractions:

7/21 + 9/21 = 16/21

So, we have:

x^{1/3} imes x^{3/7} = x^{16/21}

Finally, the result of multiplying x^{1/3} by x^{3/7} is:

x^{16/21}