Circle any terms with negative exponents. Rewrite those terms with positive exponents and move the term to the other side the fraction bar. For example, x^-3 becomes 1/(x^3) and 2/(x^-3) becomes 2(x^3). So, to factor 6(xz)^(2/3) - 4/[x^(-3/4)], the first step is to rewrite it as 6(xz)^(2/3) - 4x^(3/4).

Identify the largest common factor of all of the coefficients. For example, in 6(xz)^(2/3) - 4x^(3/4), 2 is the common factor of the coefficients (6 and 4).

Divide each term by the common factor from Step 2. Write the quotient next to the factor and separate them with brackets. For example, factoring out a 2 from 6(xz)^(2/3) - 4x^(3/4) yields the following: 2[3(xz)^(2/3) - 2x^(3/4)].

Identify any variables that appear in every term of the quotient. Circle the term in which that variable is raised to the smallest exponent. In 2[3(xz)^(2/3) - 2x^(3/4)], x appears in every term of the quotient, while z does not. You would circle 3(xz)^(2/3) because 2/3 is less than 3/4.

Factor out the variable raised to the small power found in Step 4, but not its coefficient. When dividing exponents, find the difference of the two powers and use that as the exponent in the quotient. Use a common denominator when finding the difference of two fractions. In the example above, x^(3/4) divided by x^(2/3) = x^(3/4 - 2/3) = x^(9/12 - 8/12) = x ^(1/12).

Write the result from Step 5 next to the other factors. Use brackets or parentheses to separate each factor. For example, factoring 6(xz)^(2/3) - 4/[x^(-3/4)] ultimately yields (2)[x^(2/3)][3z^(2/3) - 2x^(1/12)].