How do you simplify the expression x to the one-half power divided by x to the two-sevenths power?

To simplify the expression x^1/2 divided by x^2/7, we can use the laws of exponents. Specifically, the rule states that when you divide like bases, you subtract the exponents. Therefore, we can express this as:

x^1/2 / x^2/7 = x^{1/2 – 2/7}

Now, to perform the subtraction of the exponents 1/2 and 2/7, we first need a common denominator. The least common multiple of the denominators 2 and 7 is 14. Thus, we can convert both fractions:

• For 1/2:
  • 1/2 = 7/14
• For 2/7:
  • 2/7 = 4/14

Substituting these values back into our exponent subtraction gives us:

x^{7/14 – 4/14} = x^3/14

Thus, the simplified form of the original expression x^1/2 / x^2/7 is:

x^3/14

This shows that the original expression simplifies cleanly based on exponent rules.