1. Упростите выражение:[latex] \sqrt[6]{ (g^{3})^{9} p^{12} } [/latex] 2. Решите уравнения [latex]a) ( \frac{5}{6} )^{3x-7} = ( \frac{6}{5} )^{7x-3}[/latex] [latex]b) \sqrt{4x-3} = x [/latex]

[latex]1)\sqrt[6]{(g^3)^9p^{12}}=(g^{3*9}p^{12})^\frac{1}6=g^\frac{27}6p^\frac{12}6=g^\frac{9}2p^2=p^2\sqrt{g^9}\\\\2.a)(\frac{5}6)^{3x-7}=(\frac{6}5)^{7x-3}\\\\(\frac{6}5)^{-3x+7}=(\frac{6}5)^{7x-3}\\\\-3x+7=7x-3\\-10x=-10\\x=1\\\\2.b)\sqrt{4x-3}=x\\4x-3=x^2\\x^2-4x+3=0\\D=16-4*3=16-12=4\\\\x_1=\frac{4-2}2=1[/latex] [latex]x_2=\frac{4+2}2=3[/latex] [latex]x=1,x=3[/latex]