\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{\left(3^2\right)^{10}.5^{10}.5^{20}}{3^{15}.\left(5^2\right)^{15}}=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=3^5=243\)

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

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

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

=   \(3^2\)

a, 20 x 5 - 20/20

= 100 - 1 =99

b, 1717 - 101/2525 + 707

= 2424 - 1/25

= 60599/25

bạn ơi rút gọn mà

Trả lời:

a,\(\frac{20\times5-20}{20}\)

\(=\frac{20\times\left(5-1\right)}{20}\)

\(=\frac{20\times4}{20}\)

\(=2\)

b,\(\frac{1717-101}{2525+707}\)

\(=\frac{101\times\left(17-1\right)}{101\times\left(25+7\right)}\)

\(=\frac{101\times16}{101\times32}\)

\(=\frac{1}{2}\)

Chúc bạn học tốt

TL:

\(\frac{4.5+4.11}{4.3-8.7}=\frac{20+44}{12-56}=\frac{64}{-44}=-\frac{16}{1}=-16\)

\(\frac{4^6.3^4.9^5}{6^{12}.15}=\frac{2^{12}.3^{14}}{2^{12}.3^{13.5}}=\frac{3}{5}\)

Học tốt

-16/11và 3/5

                  Tham khảo đề bài và cách làm sau nha bạn ! 

Đề bài : Rút gọn phân số : \(\frac{4.5+4.11}{4.3-8.7}\)và \(\frac{10.7-15.8}{20.3+5.6}\)

                                                      Giải

Đặt A = \(\frac{4.5+4.11}{4.3-8.7}\)

        B = \(\frac{10.7-15.8}{20.3+5.6}\)

Ta có : A = \(\frac{4.5+4.11}{4.3-8.7}=\frac{4.\left(5+11\right)}{4.\left(3-2.7\right)}=\frac{16}{-11}\)

          : B = \(\frac{10.7-15.8}{20.3+5.6}=\frac{10.7-2.4.3.5}{2.5.2.3+5.2.3}=\frac{10.\left(7-4.3\right)}{30.\left(2+1\right)}=\frac{-5}{9}\)

Vậy A = \(\frac{16}{-11}\) ; B = \(\frac{-5}{9}\)

bạn có ghi nhầm đề ko ?

= 1,41(đã làm tròn)

Ở câu a) số mũ lúc nào cug dương mà bạn ( 45^-10 = 45¹⁰). Nếu số mũ là dương thì:

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

        = \(\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}\)

        = \(\frac{3^{20}.5^{10}.5^{20}}{3^{15}.5^{30}}\)

         = \(\frac{3^{20}.5^{30}}{3^{15}.5^{30}}\)

         = \(\frac{3^5.1}{1.1}\)

         = \(\frac{243}{1}\)

         = 243

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

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

          = \(\frac{2^{15}.3^8}{2^6.3^6.2^6}\)

          = \(\frac{2^{15}.3^8}{2^{12}.3^6}\)

          = \(\frac{2^3.3^2}{1.1}\)

          = \(\frac{8.9}{1}\)

          = \(\frac{72}{1}\)

          = 72

cảm ơn bn