Question 1133451
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There are probably different opinions about what is the "correct" way to factor an expression like this.<br>
Probably the most common interpretation is that we are supposed to remove all the common factors with fractional exponents to leave no fractional exponents in the other factor(s).  In your example,<br>
{{{4z(5z-7)^(-3/2) = ((5z-7)^(-3/2))*(4z)}}}
{{{11(5z-7)^(-1/2) = ((5z-7)^(-3/2))*(5z-7)*11}}}<br>
Then factoring out the common factor with the fractional exponents gives us<br>
{{{((5x-7)^(-3/2))*(4z+(5z-7)11)}}}
{{{((5x-7)^(-3/2))*(4z+55z-77)}}}
{{{((5x-7)^(-3/2))*(59z-77)}}}