What is factor 2(5a-1)^{3/4}+7a(5a-1)^{-1/4} ?

The solution to factor 2(5a-1)^{3/4}+7a(5a-1)^{-1/4} is (-2+17a)/((-1+5a)^{1/4)}

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factor 2(5a-1)^{3/4}+7a(5a-1)^{-1/4}

factor

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

\frac{- 2 + 17 a}{( - 1 + 5 a ) ^{\frac{1}{4}}}

Solution steps

2 (5 a - 1)^{\frac{3}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

(5 a - 1)^{\frac{3}{4}} = (5 a - 1)^{1 +- \frac{1}{4}} = (5 a - 1)^{1} (5 a - 1)^{- \frac{1}{4}}

= 2 (5 a - 1)^{1} (5 a - 1)^{- \frac{1}{4}} + 7 a (5 a - 1)^{- \frac{1}{4}}

Factor out common term

(- 1 + 5 a)^{- \frac{1}{4}}

= (- 1 + 5 a)^{- \frac{1}{4}} (2 (- 1 + 5 a) + 7 a)

Expand

7 a + 2 (5 a - 1) : - 2 + 17 a

= (17 a - 2) (5 a - 1)^{- \frac{1}{4}}

Refine

= \frac{17 a - 2}{( 5 a - 1 ) ^{\frac{1}{4}}}

6^{2} + 3^{2} = c^{2}

x + \frac{2}{3} - \frac{1}{2} (x + \frac{3}{5}) > \frac{1}{5} (x - \frac{1}{3})

2 (- 5 x + 4) + 4 x - 5 = - 3

3 x^{2} - 20 x - 63

7 - 1.5 a + (0.5 a - 5.5) = 2 a + 0.75 - (0.5 + 0.5 a)

What is factor 2(5a-1)^{3/4}+7a(5a-1)^{-1/4} ?
The solution to factor 2(5a-1)^{3/4}+7a(5a-1)^{-1/4} is (-2+17a)/((-1+5a)^{1/4)}