Tính giá trị các biểu thức. a) (4^3 . 9^7) / (27^5 . 8^2)

* Hướng dẫn giải

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

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

$=\frac{{\left(-2\right)}^{10}}{{3.2}^{12}}=\frac{2^{10}}{{3.2}^{12}}=\frac{1}{{3.2}^2}=\frac{1}{12}$

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

$=\frac{{\left(0,2\right)}^5.{\left(0,3^2\right)}^3}{{\left(0,2\right)}^7.{\left(0,3\right)}^4}=\frac{{\left(0,2\right)}^5.{\left(0,3\right)}^6}{{\left(0,2\right)}^7.{\left(0,3\right)}^4}$

$=\frac{0,3^2}{0,2^2}={\left(\frac{0,3}{0,2}\right)}^2={\left(\frac{3}{2}\right)}^2=\frac{9}{4}$

d) $\frac{2^3+2^4+2^5}{7^2}=\frac{8+16+32}{49}=\frac{56}{49}=\frac{8}{7}$