SOLUTION: Can someone please help in explaining how to correctly solve this: Factor the expression. 4z(5z − 7)^ −3/2 + 11(5z − 7)^ -1/2

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Question 1133451: Can someone please help in explaining how to correctly solve this:
Factor the expression.
4z(5z − 7)^ −3/2 + 11(5z − 7)^ -1/2
Found 3 solutions by Alan3354, greenestamps, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Can someone please help in explaining how to correctly solve this:
Factor the expression.
4z(5z − 7)^ −3/2 + 11(5z − 7)^ -1/2
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(5z - 7) is in both terms.
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You should clarify the exponents by using parantheses.
Parentheses are free.
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Equations are solved.
This it not an equation.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


There are probably different opinions about what is the "correct" way to factor an expression like this.

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,

4z%285z-7%29%5E%28-3%2F2%29+=+%28%285z-7%29%5E%28-3%2F2%29%29%2A%284z%29
11%285z-7%29%5E%28-1%2F2%29+=+%28%285z-7%29%5E%28-3%2F2%29%29%2A%285z-7%29%2A11

Then factoring out the common factor with the fractional exponents gives us

%28%285x-7%29%5E%28-3%2F2%29%29%2A%284z%2B%285z-7%2911%29
%28%285x-7%29%5E%28-3%2F2%29%29%2A%284z%2B55z-77%29
%28%285x-7%29%5E%28-3%2F2%29%29%2A%2859z-77%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Can someone please help in explaining how to correctly solve this:
Factor the expression.
4z(5z − 7)^ −3/2 + 11(5z − 7)^ -1/2
matrix%282%2C1%2C+%22+%22%2C+%285z+-+7%29%5E%28-+3%2F2%29%29 is the GCF of this expression, which leads to: