a)6 mũ 7 x 4 mũ 2 phần 9 mũ 2 x 12 mũ 5 b) 15 mũ 2 x 9 mũ 3 phần 25 mũ 3 x 27 mũ 2 c) 5 mũ 102 x 9 mũ 1009 phần 3 mũ 2018 x 25 mũ 50 d) 3 mũ 29 x 4 mũ 16 phần 27 mũ 9 x 8 mũ 11

Giải thích các bước giải:

a.Ta có:

$\dfrac{6^7\cdot 4^2}{9^2\cdot 12^5}$

$=\dfrac{(2\cdot 3)^7\cdot (2^2)^2}{(3^2)^2\cdot (2^2\cdot 3)^5}$

$=\dfrac{2^7\cdot 3^7\cdot 2^4}{3^4\cdot 2^{10}\cdot 3^5}$

$=\dfrac{2^7\cdot 2^4\cdot 3^7}{3^4\cdot 3^5\cdot 2^{10}}$

 $=\dfrac{2^{11}\cdot 3^7}{3^9\cdot 2^{10}}$

$=\dfrac{2}{3^2}$

$=\dfrac29$

b.Ta có:

$\dfrac{15^2\cdot 9^3}{25^3\cdot 27^2}$

$=\dfrac{(3\cdot 5)^2\cdot (3^2)^3}{(5^2)^3\cdot (3^3)^2}$

$=\dfrac{3^2\cdot 5^2\cdot 3^6}{5^{6}\cdot 3^{6}}$

$=\dfrac{3^8\cdot 5^2}{3^6\cdot 5^6}$

$=\dfrac{3^2}{5^4}$

$=\dfrac9{625}$

c.Ta có:

$\dfrac{5^{102}\cdot 9^{1009}}{3^{2018}\cdot 25^{50}}$

$=\dfrac{5^{102}\cdot (3^2)^{1009}}{3^{2018}\cdot (5^2)^{50}}$

$=\dfrac{5^{102}\cdot 3^{2018}}{3^{2018}\cdot 5^{100}}$

$=5^2$

$=25$

d.Ta có:

$\dfrac{3^{29}\cdot 4^{16}}{27^9\cdot 8^{11}}$

$=\dfrac{3^{29}\cdot (2^2)^{16}}{(3^3)^9\cdot (2^3)^{11}}$

$=\dfrac{3^{29}\cdot 2^{32}}{3^{27}\cdot 2^{33}}$

$=\dfrac{3^2}{2}$

$=\dfrac92$