To divide x to the 3 fourths power by x to the 1 sixth power, you can use the properties of exponents. When dividing two expressions that have the same base, you subtract the exponent of the denominator from the exponent of the numerator.
So, you start with:
x^(3/4) ÷ x^(1/6)
Using the exponent rule:
x^(a) ÷ x^(b) = x^(a – b)
In this case, a is 3/4 and b is 1/6. Therefore, you subtract:
3/4 – 1/6
To perform this subtraction, you need a common denominator. The least common multiple of 4 and 6 is 12. So convert both fractions:
- 3/4 = 9/12
- 1/6 = 2/12
Now you can subtract:
9/12 – 2/12 = 7/12
So, we have:
x^(3/4 – 1/6) = x^(7/12)
Thus, the result of dividing x to the 3 fourths power by x to the 1 sixth power is:
x^(7/12)