Bài 3:
a) \(\left(-\dfrac{2}{3}\right)^2\cdot\left(\dfrac{2}{3}\right)^5\)
\(=\left(\dfrac{2}{3}\right)^2\cdot\left(\dfrac{2}{3}\right)^5\)
\(=\left(\dfrac{2}{3}\right)^{2+5}\)
\(=\left(\dfrac{2}{3}\right)^7\)
b) \(\left(-\dfrac{1}{2}\right)^5\cdot\left(-\dfrac{1}{2}\right)^3\)
\(=\left(-\dfrac{1}{2}\right)^{5+3}\)
\(=\left(-\dfrac{1}{2}\right)^8\)
\(=\left(\dfrac{1}{2}\right)^8\)
c) \(\left(\dfrac{6}{5}\right)^7\cdot\left(-\dfrac{6}{5}\right)^4\)
\(=\left(\dfrac{6}{5}\right)^7\cdot\left(\dfrac{6}{5}\right)^4\)
\(=\left(\dfrac{6}{5}\right)^{7+4}\)
\(=\left(\dfrac{6}{5}\right)^{11}\)
Bài 4:
a) \(\left(\dfrac{3}{7}\right)^4:\left(-\dfrac{3}{7}\right)^2\)
\(=\left(\dfrac{3}{7}\right)^4\cdot\left(\dfrac{3}{7}\right)^2\)
\(=\left(\dfrac{3}{7}\right)^{4+2}\)
\(=\left(\dfrac{3}{7}\right)^6\)
b) \(\left(\dfrac{5}{9}\right)^{11}:\left(\dfrac{5}{9}\right)^7\)
\(=\left(\dfrac{5}{9}\right)^{11-7}\)
\(=\left(\dfrac{5}{9}\right)^4\)
c) \(\left(\dfrac{2}{13}\right)^7:\left(\dfrac{2}{13}\right)^5\)
\(=\left(\dfrac{2}{13}\right)^{7-5}\)
\(=\left(\dfrac{2}{13}\right)^2\)
Bài 5:
a) \(\left(\dfrac{2}{3}\right)^0\cdot\left(\dfrac{2}{3}\right)^5\)
\(=1\cdot\left(\dfrac{2}{3}\right)^5\)
\(=\left(\dfrac{2}{3}\right)^5\)
b) \(\left(\dfrac{3}{5}\right)^7\cdot\left(\dfrac{3}{5}\right)^8\)
\(=\left(\dfrac{3}{5}\right)^{7+8}\)
\(=\left(\dfrac{3}{5}\right)^{15}\)
c) \(\left(-\dfrac{2}{7}\right)^9\cdot\left(-\dfrac{2}{7}\right)^{11}\)
\(=\left(-\dfrac{2}{7}\right)^{9+11}\)
\(=\left(-\dfrac{2}{7}\right)^{20}\)