15^3+5.15^2-5^3 / 18^3+6.18^2-6^3

=3375+5.225-125 /5832+6.324-216

=3375+1125-125 /5832+1944-216

=4500-125 /7826-216

=4375 /7610

=875 /1522

mk ko bt viết phần nên viết phần bằng dấu gạch / nhé.mk cx ko bt đúng hay sai đâu nhé

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

= \(\dfrac{\left(5.3\right)^3+5.\left(5.3\right)^2-5^3}{\left(6.3\right)^3+6.\left(6.3\right)^2-6^3}\)

= \(\dfrac{5^3.3^3+5^3.3^2-5^3}{6^3.3^3+6^3.3^2-6^3}\)

= \(\dfrac{5^3.\left(3^3+3^2-1\right)}{6^3.\left(3^3+3^2-1\right)}\)

=\(\dfrac{5^3}{6^3}=\dfrac{125}{216}\)

g)\(=\left(-\dfrac{3}{4}+\dfrac{2}{5}\right).\dfrac{7}{3}+\left(\dfrac{3}{5}+-\dfrac{1}{4}\right).\dfrac{7}{3}\)
   \(=\left(-\dfrac{3}{4}+-\dfrac{1}{4}+\dfrac{2}{5}+\dfrac{3}{5}\right).\dfrac{7}{3}\)
\(=\left(-1+1\right).\dfrac{7}{3}=0.\dfrac{7}{3}=0\)

f) \(\dfrac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}\)

\(=\dfrac{3^3.5^3+5.5^2.3^2-5^3}{3^3.6^3+6.6^2.3^2-6^3}\)

\(=\dfrac{5^3.\left(3^3+3^2-1\right)}{6^3.\left(3^3+3^2-1\right)}\)

\(=\dfrac{5^3}{6^3}\)

\(=\dfrac{125}{216}\)

Gọi giá trị trên là : A

\(A=3^{100}-3^{99}+3^{98}+....+3^2-3+1\)

\(\Rightarrow3A=3^{101}-3^{100}+3^{99}-3^{98}+......+3^3-3^2+3\)

\(\Rightarrow3A+A=3^{101}+1\)

\(\Rightarrow4A=3^{101}+1\Rightarrow A=\frac{3^{101}+1}{4}\)

3³×5³+5×3²×5²-5³/ 6³+3³+ 6×6²×3²-6³=5³×(3³+3²- 1)/6³×(3³+3²-1)=5³/6³⁼125/216 

A= \(\frac{25^3.5^3}{6.5^{10}}\)= \(\frac{\left(5^2\right)^3.5^3}{6.5^{10}}\)= \(\frac{5^6.5^3}{6.5^{10}}\)= \(\frac{5^9}{6.5^{10}}\)= \(\frac{5}{6}\)

B = \(\frac{2^5.6^3}{8^2.9^2}\)= \(\frac{2^5.\left(2.3\right)^3}{\left(2^3\right)^2.\left(3^2\right)^2}\)=\(\frac{2^5.2^3.3^3}{2^6.3^4}\)= \(\frac{2^8.3^3}{2^6.3^4}\)= \(\frac{2^2}{3}\)= \(\frac{4}{3}\)

C = \(\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}\)= \(\frac{5^3.3^3+5.5^2.3^2-5^3}{6^3.3^3+6.6^2.3^2-6^3}\)= \(\frac{5^3+5^3.3^2-5^3}{6^3.3^3+6^3.3^2-6^3}\)= \(\frac{5^3.\left(1+3^2-1\right)}{6^3.\left(3^3+3^2-1\right)}\)= \(\frac{5^3.9}{6^3.35}\)    

                                                                                                                                                                                        =\(\frac{5^3.3^2}{2^3.3^3.7.5}\)

                                                                                                                                                                                       = \(\frac{25}{168}\)

D = \(\frac{\left(7^4-7^3\right)^2}{49^3}\)= \(\frac{[7^3\left(7-1\right)]^2}{\left(7^2\right)^3}\)= \(\frac{7^6.6^2}{7^6}\)= \(36\)