Power

Number

${\left(\sqrt{14\cdot \sqrt[4]{14}}\right)}^{17}$

can be written in the form

$14^x$

. Find the value of x.

Correct answer:

x =  10.625

Step-by-step explanation:

$$\begin{gathered} {\left(\sqrt{14\cdot \sqrt[4]{14}}\right)}^{17}={(14\cdot 14^{{\displaystyle \frac{1}{4}}})}^{{\displaystyle \frac{17}{2}}}={\left(14^{1+{\displaystyle \frac{1}{4}}}\right)}^{{\displaystyle \frac{17}{2}}}= \\ =14^{(1+{\displaystyle \frac{1}{4}})\cdot {\displaystyle \frac{17}{2}}} \\ x=(1+{\displaystyle \frac{1}{4}})\cdot {\displaystyle \frac{17}{2}} \\ x=10.625 \end{gathered}$$

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