# Power

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

Result

x =  4.95

#### Solution:

$\left( \sqrt{ 7 \cdot \sqrt[ 10 ] { 7 } } \right)^{ 9 } = \left( 7 \cdot 7^ { \dfrac{1}{ 10} } \right)^{ \dfrac{ 9 }{2}} = \left( 7^ { 1 + \dfrac{1}{ 10} } \right)^{ \dfrac{ 9 }{2}} = \ \\ = 7^ { (1 + \dfrac{1}{ 10})\cdot \dfrac{ 9 }{2} } \ \\ x = 4.95 \ \\$

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