Question

I dont even need help with the question.

Answer 1

`32^{(1)/(25)}\cdot 2^x ~~ = ~~8^{(1)/(4)}\implies (2^5)^{(1)/(25)}\cdot 2^x~~ = ~~(2^3)^{(1)/(4)}\implies 2^{(5)/(25)}\cdot 2^x~~ = ~~2^{(3)/(4)} \\\\\\ \stackrel{same~exponent}{\underset{same~base}{2^{(5)/(25)+x}~~ = ~~2^{(3)/(4)}}}\implies \cfrac{5}{25}+x~~ = ~~\cfrac{3}{4}\implies \cfrac{1}{5}+x~~ = ~~\cfrac{3}{4}`

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{1}{5}+x \right)~~ = ~~20\left( \cfrac{3}{4} \right)}\implies 4+20x~~ = ~~15 \\\\\\ 20x=11\implies {\Large \begin{array}{llll} x=\cfrac{11}{20} \end{array}}`