Power

Number
(7⋅710)9 \left( \sqrt{ 7 \cdot \sqrt[ 10 ] { 7 } } \right)^{ 9 }
can be written in the form
7x7^x
. Find the value of x.

Result

x =  4.95

Solution:

(7⋅710)9=(7⋅7110)92=(71+110)92= =7(1+110)⋅92 x=4.95  \left( \sqrt{ 7 \cdot \sqrt[ 10 ] { 7 } } \right)^{ 9 } = \left( 7 \cdot 7^ { \dfrac{1}{ 10} } \right)^{ \dfrac{ 9 }{2}} = \left( 7^ { 1 + \dfrac{1}{ 10} } \right)^{ \dfrac{ 9 }{2}} = \ \\ = 7^ { (1 + \dfrac{1}{ 10})\cdot \dfrac{ 9 }{2} } \ \\ x = 4.95 \ \\

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