Bài 6: Thực hiện phép tính.
\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{5^{16}.\left(3^3\right)^7}{\left(5^3\right)^5.\left(3^2\right)^{11}}=\dfrac{5^{16}.3^{21}}{5^{15}.3^{22}}=\dfrac{5}{3}\)
\(b,\left(-0,2\right)^2.5-\dfrac{2^3.27^3}{4^6.9^5}=0,04.5-\dfrac{2^3.\left(3^3\right)^3}{\left(2^2\right)^6.\left(3^2\right)^5}=0,2-\dfrac{2^3.3^9}{2^{12}.3^{10}}=\dfrac{1}{5}-\dfrac{1}{2^9.3}=\dfrac{1}{5}-\dfrac{1}{512.3}=\dfrac{1}{5}-\dfrac{1}{1536}=\dfrac{1536}{7680}-\dfrac{5}{7680}=\dfrac{1531}{7680}\)
\(c,\dfrac{5^6+2^2.25^3+2^3.125^2}{26.5^6}\)
\(=\dfrac{5^6+2^2.\left(5^2\right)^3+2^3.\left(5^3\right)^2}{26.5^6}\)
\(=\dfrac{5^6+2^2.5^6+2^3.5^6}{26.5^6}\)
\(=\dfrac{5^6.\left(1+2^2+2^3\right)}{26.5^6}\)
\(=\dfrac{5^6.13}{26.5^6}\)
\(=\dfrac{13}{26}=\dfrac{1}{2}\)
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