\(a,\left(\dfrac{7}{3}\right)^3:\left(-\dfrac{35}{9}\right)^3\)
\(=\left(\dfrac{7}{3}:-\dfrac{35}{9}\right)^3\)
\(=\left(\dfrac{7}{3}\cdot-\dfrac{9}{35}\right)^3\)
\(=\left(\dfrac{1}{1}\cdot-\dfrac{3}{5}\right)^3\)
\(=\left(-\dfrac{3}{5}\right)^3\)
\(=\left(-\dfrac{27}{125}\right)\)
\(b,125\cdot5^2\cdot\dfrac{1}{625}\cdot5^3\)
\(=5^3\cdot5^2\cdot\dfrac{1}{5^4}\cdot5^3\)
\(=5^5\cdot\dfrac{1}{5^4}\cdot5^3\)
\(=5\cdot1\cdot5^3\)
\(=5^4=625\)
\(c,8\cdot32:\left(2^4\cdot\dfrac{1}{32}\right)\)
\(=2^3\cdot2^5:\left(2^4\cdot\dfrac{1}{2^5}\right)\)
\(=2^3\cdot2^5:\left(1\cdot\dfrac{1}{2}\right)\)
\(=2^3\cdot2^5:\dfrac{1}{2}\)
\(=2^8\cdot2\)
\(=2^9\)
\(d,6^3\cdot5^2\cdot\left(\dfrac{5}{6}\right)^3\)
\(=6^3\cdot5^2\cdot\dfrac{\left(5\right)^3}{\left(6\right)^3}\)
\(=216\cdot25\cdot\dfrac{125}{216}\)
\(=5400\cdot\dfrac{125}{216}\)
\(=3125\)
\(a,\left(\dfrac{7}{3}\right)^3:\left(\dfrac{-35}{9}\right)^3\)
\(=\left(\dfrac{7}{3}:\dfrac{-35}{9}\right)^3\)
\(=\left(\dfrac{7}{3}.\dfrac{-9}{35}\right)^3\)
\(=\left(\dfrac{1.\left(-3\right)}{1.5}\right)^3\)
\(=\left(\dfrac{-3}{5}\right)^3\)
\(=\dfrac{\left(-3\right)^3}{5^3}\)
\(\dfrac{-27}{125}\)
\(b,125.5^2.\dfrac{1}{625}.5^3\)
\(=5^3.5^2.5^{-4}.5^3\)
\(=5^{3+2+\left(-4\right)+3}\)
\(=5^4\)
\(c,8.32:\left(2^4.\dfrac{1}{32}\right)\)
\(=2^3.2^5:\left(2^4.2^{-5}\right)\)
\(=2^{3+5}:\left(2^{4+\left(-5\right)}\right)\)
\(=2^8:2^{-1}\)
\(=2^{8-\left(-1\right)}\)
\(=2^9\)
\(d,6^3.5^2.\left(\dfrac{5}{6}\right)^3\)
\(=6^3.5^2.\dfrac{5^3}{6^3}\)
\(=6^3.5^2.5^3:6^3\)
\(=6^3:6^3.5^2.5^3\)
\(=1.5^{2+3}\)
\(=5^5\)
