SOLUTION: Factor while dealing with negative and fractional exponents: (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4 {{{ (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4 }}}

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Factor while dealing with negative and fractional exponents: (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4 {{{ (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4 }}}      Log On


   

Question 1121808: Factor while dealing with negative and fractional exponents: (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4
+%285%2F3%29x%5E%28-1%2F4%29%28x-7%29%5E3%2B2x%5E%28-5%2F4%29%28x-7%29%5E4+
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


There are powers of x and of (x-7) in both terms. Factor out the smaller power of each from both terms.

-5/4 is smaller than -1/4; 3 is smaller than 4. So factor out x^(-5/4) and (x-7)^3:

+%285%2F3%29x%5E%28-1%2F4%29%28x-7%29%5E3%2B2x%5E%28-5%2F4%29%28x-7%29%5E4+

= %28x%5E%28-5%2F4%29%2A%28x-7%29%5E3%29%28%285%2F3%29x%2B2%28x-7%29%29

= %28x%5E%28-5%2F4%29%2A%28x-7%29%5E3%29%28%285%2F3%29x%2B2x-14%29

= %28x%5E%28-5%2F4%29%2A%28x-7%29%5E3%29%28%2811%2F3%29x-14%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Factor while dealing with negative and fractional exponents: (5/3)x^(-1/4)(x-7)^3+2x^(-5/4)(x-7)^4
+%285%2F3%29x%5E%28-1%2F4%29%28x-7%29%5E3%2B2x%5E%28-5%2F4%29%28x-7%29%5E4+


 ---- Multiplying expression by LCD, 3 to get rid of fraction

matrix%282%2C1%2C+%22+%22%2C+x%5E%28-+5%2F4%29%28x+-+7%29%5E3%285x+%2B+6%28x+-+7%29%29%29 --------- Factoring out, GCF, matrix%282%2C1%2C+%22+%22%2C+x%5E%28-+5%2F4%29%28x+-+7%29%5E3%29