How do you divide x to the 3/4 power by x to the 1/6 power?

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To divide x to the 3/4 power by x to the 1/6 power, you can use the laws of exponents. According to the law of exponents, when you divide two numbers with the same base, you subtract their exponents.

So, in this case, you have:

x^(3/4) / x^(1/6) = x^(3/4 - 1/6)

Next, you need to calculate 3/4 – 1/6. To do this, first find a common denominator. The least common denominator of 4 and 6 is 12.

Now, convert each fraction:

  • 3/4 becomes (3 * 3)/(4 * 3) = 9/12
  • 1/6 becomes (1 * 2)/(6 * 2) = 2/12

Now, you can subtract:

9/12 - 2/12 = 7/12

This means:

x^(3/4) / x^(1/6) = x^(7/12)

So, the final answer is:

x^(7/12)

In summary, when dividing x to the power of 3/4 by x to the power of 1/6, you subtract the exponents to get x raised to the 7/12 power.

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