Question

TÍNH GIÁ TRỊ CÁC BIỂU THỨC:

a) \(A=\frac{25^3.5^5}{6.5^{10}}\)

b) \(B=\frac{2^5.6^3}{8^2.9^2}\)

C) \(C=\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}\)

 

Answer 1

\(A=\frac{25^3.5^5}{6.5^{10}}=\frac{\left(5^2\right)^3.5^5}{6.5^{10}}=\frac{5^6.5^5}{6.5^{10}}=\frac{5^{11}}{6.5^{10}}=\frac{5}{6}\)

Answer 2

\(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.2^3.3^3}{\left(2^3\right)^2.\left(3^2\right)^2}=\frac{2^8.3^3}{2^6.3^4}=\frac{4}{3}\)

Answer 3

\(A=\frac{25^3.5^3}{6.5^{10}}=\frac{5^6.5^3}{6.5^{10}}=\frac{5^9}{6.5.5^9}=\frac{1}{30}\)
\(B=\frac{2^5.6^3}{8^2.9^2}=\frac{2^5.2^3.3^3}{2^6.3^4}=\frac{2^8.3^3}{2^6.3^4}=\frac{2^2}{3}=\frac{4}{3}\)
\(C=\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}=\frac{5^3\left(3^3+3^2-1\right)}{6^3\left(3^3+3^2-1\right)}=\frac{5^3}{6^3}\)

Answer 4

\(A=\frac{25^3\cdot5^5}{6\cdot5^{10}}=\frac{\left(5^2\right)^3\cdot5^5}{6\cdot5^{10}}=\frac{5^6\cdot5^5}{6\cdot5^{10}}=\frac{5^{11}}{5\cdot5^{10}}=\frac{5}{6}\)

\(B=\frac{2^5\cdot6^3}{8^2\cdot9^2}=\frac{2^5\cdot2^3\cdot3^3}{\left(2^3\right)^2\cdot\left(3^2\right)^2}=\frac{2^8\cdot3^3}{2^6\cdot3^4}=\frac{2^2}{3}=\frac{4}{3}\)

\(C=\frac{15^3+5\cdot15^2-5^3}{18^3+6\cdot18^2-6^3}=\frac{5^3\cdot3^3+5\cdot5^2\cdot3^2-5^3}{6^3\cdot3^3+6\cdot6^2\cdot3^2-6^3}=\frac{5^3\left(3^3+3^2-1\right)}{6^3\left(3^3+3^2-1\right)}=\frac{5^3}{6^3}\)