Giải bài 8 trang 21

Đề bài

Tính giá trị các biểu thức.

a)$\frac{4^3{.9}^7}{{27}^5{.8}^2};$                  

b)$\frac{{\left(-2\right)}^3.{\left(-2\right)}^7}{{3.4}^6};$

c)$\frac{{\left(0,2\right)}^5.{\left(0,09\right)}^3}{{\left(0,2\right)}^7.{\left(0,3\right)}^4};$     

d)$\frac{2^3+2^4+2^5}{7^2}.$

Lời giải chi tiết

a) $\frac{4^3{.9}^7}{{27}^5{.8}^2}$ $=\frac{{\left(2^2\right)}^3.{\left(3^2\right)}^7}{{\left(3^3\right)}^5.{\left(2^3\right)}^2}$ $=\frac{2^{2.3}{.3}^{2.7}}{3^{3.5}{.2}^{2.3}}$ $=\frac{2^6{.3}^{14}}{3^{15}{.2}^6}$ $=\frac{1}{3}$

b) $\frac{{\left(-2\right)}^3.{\left(-2\right)}^7}{{3.4}^6}$ $=\frac{(-2{)}^{3+7}}{3.(2^2{)}^6}$ $=\frac{{\left(-2\right)}^{10}}{3.\left(2^{2.6}\right)}$ $=\frac{2^{10}}{{3.2}^{12}}$ $=\frac{1}{{3.2}^2}$ $=\frac{1}{12}$

c) $\frac{{\left(0,2\right)}^5.{\left(0,09\right)}^3}{{\left(0,2\right)}^7.{\left(0,3\right)}^4}$ $=\frac{{\left(0,2\right)}^5.{\left[{\left(0,3\right)}^2\right]}^3}{{\left(0,2\right)}^7.{\left(0,3\right)}^4}$ $=\frac{{\left(0,2\right)}^5.{\left(0,3\right)}^6}{{\left(0,2\right)}^7.{\left(0,3\right)}^4}$ $=\frac{{\left(0,3\right)}^2}{{\left(0,2\right)}^2}$ $=\frac{0,09}{0,04}$ $=\frac{9}{4}$

d)

Cách 1: $\frac{2^3+2^4+2^5}{7^2}$ $=\frac{8+16+32}{49}$ $=\frac{56}{49}$ $=\frac{8}{7}$

Cách 2: $\frac{2^3+2^4+2^5}{7^2}$ $=\frac{2^3.(1+2+2^2)}{7^2}$ $=\frac{2^3.7}{7^2}$ $=\frac{8}{7}$