Giải bài 3 trang 27

Đề bài

Thực hiện phép tính.

a) $\frac{5^{16}{.27}^7}{{125}^5{.9}^{11}}$         b)${\left(-0,2\right)}^2.5-\frac{2^{13}{.27}^3}{4^6{.9}^5};$

c)$\frac{5^6+2^2{.25}^3+2^3{.125}^2}{{26.5}^6}.$

Lời giải chi tiết

a)

$\frac{5^{16}{.27}^7}{{125}^5{.9}^{11}}=\frac{5^{16}.{\left(3^3\right)}^7}{{\left(5^3\right)}^5.{\left(3^2\right)}^{11}}=\frac{5^{16}{.3}^{21}}{5^{15}{.3}^{22}}=\frac{5.5^{15}{.3}^{21}}{5^{15}.3{.3}^{21}}=\frac{5}{3}$

b)

${\left(-0,2\right)}^2.5-\frac{2^{13}{.27}^3}{4^6{.9}^5}=0,04.5-\frac{2^{13}.{\left(3^3\right)}^3}{{\left(2^2\right)}^6.{\left(3^2\right)}^5}=0,2-\frac{2^{13}{.3}^9}{2^{12}{.3}^{10}}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=\frac{-7}{15}$

c)

$\begin{array}{c}\frac{5^6+2^2{.25}^3+2^3{.125}^2}{{26.5}^6}=\frac{5^6+2^2.{\left(5^2\right)}^3+2^3.{\left(5^3\right)}^2}{{\mathrm{2.13.5}}^6}\\ =\frac{5^6+{4.5}^6+{8.5}^6}{{\mathrm{2.13.5}}^6}=\frac{5^6.\left(1+4+8\right)}{{\mathrm{2.13.5}}^6}\\ =\frac{5^6.13}{{\mathrm{2.13.5}}^6}=\frac{1}{2}\end{array}$