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\(\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{29}\cdot9^{10}-7\cdot2^{29}\cdot27^6}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^2\cdot2^{27}\cdot3^{20}}{5\cdot2^{29}\cdot3^{20}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot3^2-7\right)}\)
\(=\dfrac{10-9}{5\cdot9-7}=\dfrac{1}{38}\)
b) (5/2-3x)=25/9
3x = 5/2-25/9
3x =-5/18
x =-5/18:3
x=-5/54
\(e.\left(x-1\right)^5=-32\)
\(\left(x-1\right)^5=\left(-2\right)^5\)
\(x-1=-2\)
\(x\) \(=-2+1\)
\(x\) \(=-1\)
Vậy \(x=-1\)
[6⁸.(-4)³]/(9⁴.12⁶)
= (-2⁸.3⁸.2⁶)/(3⁸.2⁶.3⁶)
= -(2¹⁴.3⁸)/(2⁶.3¹⁴)
= - 2⁸/3⁶
= -256/729
\(\left(\dfrac{9}{4}\right)^3.\left(\dfrac{12}{9}\right)^0:\left(-\dfrac{9}{8}\right)^3=\left(\dfrac{9}{4}\right)^3.1:\left(-\dfrac{9}{8}\right)^3\)
\(=\left(\dfrac{9}{4}:\dfrac{-9}{8}\right)^3=\left(-2\right)^3=-8\)