a.

\(\frac{45^{10}\times5^{20}}{75^{15}}=\frac{\left(3^2\times5\right)^{10}\times5^{20}}{\left(3\times5^2\right)^{15}}=\frac{3^{20}\times5^{10}\times5^{20}}{3^{15}\times5^{30}}=3^5=243\)

b.

\(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,8\right)^5}{\left(0,4\right)^5}\times\frac{1}{\left(0,4\right)}=\left(\frac{0,8}{0,4}\right)^5\times\frac{1}{\frac{4}{10}}=2^5\times\frac{5}{2}=2^4\times5=16\times5=80\)

c.

\(\frac{2^{15}\times9^4}{6^6\times8^3}=\frac{2^{15}\times\left(3^2\right)^4}{\left(2\times3\right)^6\times\left(2^3\right)^3}=\frac{2^{15}\times3^8}{2^6\times3^6\times2^9}=3^2=9\)

Chúc bạn học tốt ^^

tớ cũng đang học cái đấy nè

     225^10

a = _________  = 3^10

      75^10

       2^15 * 3^8             2^15 * 3^8

c=  _____________= --------------------  =2^3 * 3^5

      2^3 * 3^3 * 2^9       2^12 * 3^3

tớ có 1 bài giống y cậu nè

mình làm bài này rồi nè

1. sai dấu nhé 

2.a, \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5=243\)

b, \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(\frac{4}{5}\right)^5}{\left(\frac{2}{5}\right)^6}=\frac{\left(\frac{2}{5}\cdot2\right)^5}{\left(\frac{2}{5}\right)^6}=\frac{\left(\frac{2}{5}\right)^5\cdot2^5}{\left(\frac{2}{5}\right)^5\cdot\frac{2}{5}}=2^5\div\frac{2}{5}=32\cdot\frac{5}{2}=80\)

c, \(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^2}{2^{15}}=3^2=9\)

a) A = \(\frac{45^{10}.5^{10}}{75^{10}}=\frac{\left(5.3^2\right)^{10}.5^{10}}{\left(5^2.3\right)^{10}}=\frac{5^{10}.3^{20}.5^{10}}{5^{20}.3^{10}}=\frac{5^{20}.3^{10}}{5^{20}}=3^{10}=59049\)

b) B = \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,2.2^2\right)^5}{\left(0,2.2\right)^6}=\frac{\left(0,2\right)^5.2^{10}}{\left(0,2\right)^6.2^6}=\frac{2^4}{0,2}=\frac{16}{0,2}=80\)

c) C = \(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^2}{2^{15}}=3^2=9\)

\(A=\frac{\left(9^{10}×5^{10}×5^{10}\right)}{\left(25^{10}×3^{10}\right)}\)

\(A=\frac{\left(3^{20}×5^{20}\right)}{\left(5^{20}×3^{10}\right)}\)

\(A=\frac{3^{20}}{3^{10}}\)

\(A=3^{10}\)

a) \(\frac{45^{10}.5^{20}}{75^{15}}\)

=
\(\frac{\left(5.9\right)^{10}.5^{20}}{\left(5.15\right)^{15}}\)

=  \(\frac{5^{10}.9^{10}.5^{20}}{5^{15}.15^{15}}\)

=    \(\frac{5^{10}.3^{20}.5^{20}}{5^{15}.15^{15}}\)

=    \(\frac{5^{10}.15^{20}}{5^{15}.15^{15}}\)

=     \(\frac{15^5}{5^5}\)

=     \(\frac{3^5.5^5}{5^5}\)

= \(3^5\)

b) \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}\)

=   \(\frac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)

=    \(\frac{2^5}{0,4}\)

= \(2^5\) : 0,4

(=) 32 : \(\frac{2}{5}\)

= 90

c) \(\frac{2^{15}.9^4}{6^6.8^3}\)

=  \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}\)

=    \(\frac{2^{15}.3^8}{2^6.3^6.2^9}\)

=   \(3^2\)

=\(\left[\dfrac{\left(0,4.2\right)^5}{\left(0,4\right)^6}+\dfrac{2^9.2^6.3^8}{\left(3.2\right)^6.2^9}\right]=\left[\dfrac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}+\dfrac{2^6.3^8}{3^6.2^6}\right]\)

=\(\left[\dfrac{2^5}{0,4}+3^2\right]\)

=\(\left[80+9\right]=89\)

\(\left[\dfrac{\left(2.0,4\right)^5}{0,4,0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^6.2^9}\right]\div\dfrac{3^{20}.5^{30}}{3^{15}.5^{30}}\)

\(=\left[\dfrac{2^5.0.4^5}{0,4.0,4^5}+\dfrac{2^{15}.3^8}{3^6.2^{15}}\right]\div3^5\)

\(=\left[\dfrac{2^5}{0,4}+3^2\right]\div243\)

\(=80+\left(3^5\div3^2\right)\)

\(=80+3^3\)

\(=80+27\)

\(=107\)

a,243

b,80

c,9