\(\frac{45^{10}\times5^{20}}{75^{15}}=243\)

mk ko nhớ cách giải, chỉ có kết quả, nếu đúng k cho mk nha

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{5^{10}.3^{20}.5^{20}}{3^{15}.5^{30}}=\frac{5^{30}.3^{20}}{3^{15}.5^{30}}=3^7=243\)

\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{3^{20}\times5^{10}\times5^{20}}{3^{15}\times5^{30}}=3^5=243\)

bằng 3

1 — 1 + 1 + 1 + 1

= 0 + 1 + 1 + 1

= 3

\(\frac{45^{10}.5^{20}}{75^5}\)

\(=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(5^2.3\right)^5}\)

\(=\frac{3^{20}.5^{10}.5^{20}}{5^{10}.3^5}\)

\(=3^{15}.5^{20}\)

\(\frac{45^{10}.5^{20}}{75^5}=\frac{9^{10}.5^{10}.5^{20}}{25^5.3^5}=\frac{3^{20}.5^{10}.5^{20}}{5^{10}.3^5}=\frac{3^{20}.5^{30}}{5^{10}.3^5}=3^{15}.5^{20}\)

a.=[ \(\frac{1}{5}\)x 5 ]⁵            b. \(\frac{102^3}{40^3}\)=[ \(\frac{102}{40}\)]^{3                       c.=\(\frac{75^{10}.5^{20}}{75^{10}.75^5}\)=}\(\frac{5^{20}}{75^5}\)  

=1^{5                                                                 =[} \(\frac{51}{20}\)]³                                                 

⁼¹

Bài 1:
a)

\(\frac{8^{20}+4^{20}}{4^{25}+64^5}=\frac{(2^3)^{20}+(2^2)^{20}}{(2^2)^{25}+(2^6)^{5}}=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}=\frac{2^{40}(2^{20}+1)}{2^{30}(2^{20}+1)}=2^{10}\)

b)

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{(3^2.5)^{10}.5^{20}}{(3.5^2)^{15}}=\frac{3^{20}5^{30}}{3^{15}.5^{30}}=\frac{3^{20}}{3^{15}}=3^5\)

Bài 2:

Ta thấy $(x-2)^{2012}=[(x-2)^{1006}]^2\geq 0$ với mọi $x\in\mathbb{R}$

$|b^2-9|^{2014|\geq 0$ với mọi $b\in\mathbb{R}$ (tính chất trị tuyệt đối)

Do đó để tổng của chúng bằng $0$ thì:

\((x-2)^{2012}=|b^2-9|^{2014}=0\)

\(\Leftrightarrow \left\{\begin{matrix} x-2=0\\ b^2-9=0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x=2\\ b=\pm 3\end{matrix}\right.\)

Vậy.......

\(\frac{45^{10}20^{10}}{75^{15}}\)=\(\frac{1125^{10}}{75^5.75^{10}}\)=\(\frac{1125^{10}}{75}\)=\(\frac{1}{75^5}\)=\(\frac{15^{10}}{75^5}\)=\(\frac{15^5.15^5}{75^5}\)=\(\frac{15^5}{75}\).\(15^5\)=\(\frac{1^5}{3}\).\(15^5\)=\(\frac{1}{3}.15^5\)=\(^{5^5}\)=3125

\(\frac{4^{10}.20^{10}}{75^{15}}\)

\(=\frac{1125^{10}}{75^5.75^{10}}\)

\(=\frac{1125^{10}}{75}\)

\(=\frac{1}{75^5}\)

\(=\frac{15^{10}}{75^5}\)

\(=\frac{15^5.15^5}{75^5}\)

\(=\frac{15^5}{75}.15^5\)

\(=\frac{1}{3}^5.15^5\)

\(=\frac{1}{3}.15^5\)

\(=^{5^5}\)

\(=3125\)

\(4^{10}\times20^{10}=1125^{10}\) ????????????