Question

15. Tính:

a) \(\frac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)

b) \(\frac{\left(\frac{2}{7}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)

mình cần lắm ạ, tối nay phải nộp rồi cám ơn các bn trc :''(

Answer 1

15: Tính

a) Ta có: \(\frac{3^6\cdot45^4-15^{13}\cdot5^{-9}}{27^4\cdot25^3+45^6}\)

\(=\frac{3^6\cdot3^4\cdot15^4-15^{13}\cdot\frac{1}{5^9}}{9^4\cdot3^4\cdot5^6+9^6\cdot5^6}\)

\(=\frac{3^6\cdot45^4-\frac{5^{13}\cdot3^{13}}{5^9}}{9^4\cdot5^6\left(3^4+9^2\right)}\)

\(=\frac{45^4\cdot3^6-5^4\cdot3^{13}}{45^4\cdot5^2\cdot2\cdot9^2}\)

\(=\frac{5^4\cdot3^6\left(9^4-3^7\right)}{5^2\cdot3^4\cdot45^4\cdot2}\)

\(=\frac{5^2\cdot3^2\cdot\left(3^8-3^7\right)}{45^4\cdot2}\)

\(=\frac{5^2\cdot3^9\cdot\left(3-1\right)}{5^4\cdot3^8\cdot2}\)

\(=\frac{1}{5^2}\cdot3\)

\(=\frac{3}{25}\)