Question Number 66760 by John Kaloki Musau last updated on 19/Aug/19
$${By}\:{writing}\:{your}\:{answer}\:{in}\:{the} \\ $$$${form}\:{a}^{{y}} \:{simplify} \\ $$$$\left(\mathrm{3}^{\mathrm{5}{x}} ×\mathrm{5}^{\mathrm{2}{x}} ×\mathrm{3}^{−{x}} \boldsymbol{\div}\mathrm{5}^{−\mathrm{2}{x}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} \\ $$
Commented by Prithwish sen last updated on 19/Aug/19
$$\mathrm{15}^{\mathrm{x}} \\ $$
Commented by John Kaloki Musau last updated on 20/Aug/19
$${how}\:{did}\:{u}\:{do}\:{it}? \\ $$
Answered by Kunal12588 last updated on 20/Aug/19
$$\left(\frac{\mathrm{3}^{\mathrm{5}{x}} ×\mathrm{5}^{\mathrm{2}{x}} ×\mathrm{3}^{−{x}} }{\mathrm{5}^{−\mathrm{2}{x}} }\right)^{\mathrm{1}/\mathrm{4}} \\ $$$$=\left(\mathrm{3}^{\mathrm{5}{x}−{x}} ×\mathrm{5}^{\mathrm{2}{x}+\mathrm{2}{x}} \right)^{\mathrm{1}/\mathrm{4}} \\ $$$$=\left(\mathrm{3}^{\mathrm{4}{x}} ×\mathrm{5}^{\mathrm{4}{x}} \right)^{\mathrm{1}/\mathrm{4}} \\ $$$$=\mathrm{15}^{\mathrm{4}{x}×\frac{\mathrm{1}}{\mathrm{4}}} \\ $$$$=\mathrm{15}^{{x}} \\ $$
Commented by John Kaloki Musau last updated on 21/Aug/19
$${I}\:{like}\:{it} \\ $$
Answered by Mr Jor last updated on 25/Aug/19
$$\left(\mathrm{3}^{\mathrm{5}\boldsymbol{{x}}−\boldsymbol{{x}}} ×\mathrm{5}^{\mathrm{2}\boldsymbol{{x}}−\left(−\mathrm{2}\boldsymbol{{x}}\right)} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} \\ $$$$\left(\mathrm{3}^{\mathrm{4}\boldsymbol{{x}}} ×\mathrm{5}^{\mathrm{4}\boldsymbol{{x}}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} =\mathrm{3}^{\mathrm{4}\boldsymbol{{x}}×\frac{\mathrm{1}}{\mathrm{4}}} ×\mathrm{5}^{\mathrm{4}\boldsymbol{{x}}×\frac{\mathrm{1}}{\mathrm{4}}} \\ $$$$\mathrm{3}^{\boldsymbol{{x}}} ×\mathrm{5}^{\boldsymbol{{x}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{15}^{\boldsymbol{{x}}} \\ $$