Question

sqrt{125^x} = 5/25^x

Answer 1

hm?

Answer 2

thats alright. want me to put my other questions here?

Answer 3

\[\Large \sqrt{125^x} = \frac{5}{25^x}\]


\[\Large \sqrt{\left(5^3\right)^x} = \frac{5^1}{\left(5^3\right)^x}\]


\[\Large \sqrt{5^{3x}} = \frac{5^1}{5^{2x}}\]


\[\Large \left(5^{3x}\right)^{\frac{1}{2}} = \frac{5^1}{5^{2x}}\]


\[\Large 5^{\frac{3x}{2}} = \frac{5^1}{5^{2x}}\]


\[\Large 5^{\frac{3x}{2}} = 5^{1-2x}\]


\[\Large \frac{3x}{2} = 1-2x\]


\[\Large \frac{3x}{2}+2x = 1\]


\[\Large \frac{7x}{2} = 1\]


\[\Large 7x = 2\]


\[\Large x = \frac{2}{7}\]