Question

find the value of x in each of the following
1024/3125=x5​

Answer 1

Step-by-step explanation:

....................

Answer 2

Answer:

$\displaystyle\frac{1024}{3125}=x^5\quad :\quad x=\frac{4}{5}\quad \left(\mathrm{Decimal}:\quad x=0.8\right)$

Step-by-step explanation:

$\displaystyle\frac{1024}{3125}=x^5$

$\gray{\mathrm{Switch\:sides}}$

$\displaystyle x^5=\frac{1024}{3125}$

$\gray{\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:odd,\:the\:solution\:is\:}x=\sqrt[n]{f\left(a\right)}}$

$\displaystyle x=\sqrt[5]{\frac{1024}{3125}}$

$\displaystyle\black{\sqrt[5]{\frac{1024}{3125}}}$

$\displaystyle\gray{\mathrm{Apply\:radical\:rule\:}\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0}$

$\displaystyle=\frac{\sqrt[5]{1024}}{\sqrt[5]{3125}}$

$\gray{\sqrt[5]{3125}=5}$

$\displaystyle=\frac{\sqrt[5]{1024}}{5}$

$\gray{\sqrt[5]{1024}=4}$

$\displaystyle=\frac{4}{5}$

$\displaystyle x=\frac{4}{5}$