What is factor 49x^{-9/2}+14x^{-7/2}+x^{-5/2} ?

The solution to factor 49x^{-9/2}+14x^{-7/2}+x^{-5/2} is ((x+7)^2)/(x^{9/2)}

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factor 49x^{-9/2}+14x^{-7/2}+x^{-5/2}

factor

49 x^{- \frac{9}{2}} + 14 x^{- \frac{7}{2}} + x^{- \frac{5}{2}}

\frac{( x + 7 ) ^{2}}{x ^{\frac{9}{2}}}

Solution steps

49 x^{- \frac{9}{2}} + 14 x^{- \frac{7}{2}} + x^{- \frac{5}{2}}

Rewrite as

= 7 \cdot 7 x^{- \frac{9}{2}} + 7 \cdot 2 x^{- \frac{7}{2}} + x^{- \frac{5}{2}}

Factor out common term

7

= 7 (7 x^{- \frac{9}{2}} + 2 x^{- \frac{7}{2}}) + x^{- \frac{5}{2}}

Factor

7 x^{- \frac{9}{2}} + 2 x^{- \frac{7}{2}} : \frac{7 + 2 x}{x ^{\frac{9}{2}}}

= x^{- \frac{5}{2}} + 7 \cdot \frac{2 x + 7}{x ^{\frac{9}{2}}}

Apply exponent rule:

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

x^{- \frac{7}{2}} = x^{1 +- \frac{9}{2}} = x^{1} x^{- \frac{9}{2}}, x^{- \frac{5}{2}} = x^{2 +- \frac{9}{2}} = x^{2} x^{- \frac{9}{2}}

= 49 x^{- \frac{9}{2}} + 14 x^{1} x^{- \frac{9}{2}} + x^{2} x^{- \frac{9}{2}}

Factor out common term

x^{- \frac{9}{2}}

= x^{- \frac{9}{2}} (49 + 14 x + x^{2})

Factor

x^{2} + 14 x + 49 : (x + 7)^{2}

= x^{- \frac{9}{2}} (x + 7)^{2}

Refine

= \frac{( x + 7 ) ^{2}}{x ^{\frac{9}{2}}}

10 \cdot 6

22 \cdot 2 x + 33 \cdot 2

8^{\frac{5}{2}}

y^{4} - 81

216 x^{3} + 1000

What is factor 49x^{-9/2}+14x^{-7/2}+x^{-5/2} ?
The solution to factor 49x^{-9/2}+14x^{-7/2}+x^{-5/2} is ((x+7)^2)/(x^{9/2)}