Find the value of {(9^3+9^4+9^5+9^6+9^7)/(9^1+9^2+9^3+9^4+9^5)}^(1/2)

Question : Find the value of $ \left(\cfrac{9^3+9^4+9^5+9^6+9^7}{9^1+9^2+9^3+9^4+9^5}\right)^{\cfrac{1}{2}}$

9

3

729

81

Solution: $\require{cancel}$

$ \left(\cfrac{9^3+9^4+9^5+9^6+9^7}{9^1+9^2+9^3+9^4+9^5}\right)^{\cfrac{1}{2}}$
= $ \left(\cfrac{9^2\cancel{(9^1+9^2+9^3+9^4+9^5)}}{\cancel{(9^1+9^2+9^3+9^4+9^5)}}\right)^{\cfrac{1}{2}}$
= $ 9^{\cancel{2} \times \cfrac{1}{\cancel{2}}}$
= $ 9 $

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