tính \(\frac{25^4.16^3.3^7}{75^4.6^3.8^2}\)
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Đặt \(A=\frac{25^3.3+25^3.5}{2^{27}}\)
Ta có:\(A=\frac{25^3\left(3+5\right)}{2^{27}}\)
\(A=\frac{25^3.8}{2^{27}}\)
\(A=\frac{25^3.2^3}{\left(2^9\right)^3}\)
\(A=\frac{50^3}{512^3}\)
\(A=\left(50:512\right)^3\)
\(A=\left(\frac{25}{256}\right)^3\)
Vậy \(A=\left(\frac{25}{256}\right)^3\)

a. \(-\frac{13}{6}:\frac{25}{7}+\frac{7}{25}.\left(-\frac{17}{6}\right)\)
\(=-\frac{13}{6}.\frac{7}{25}+\frac{7}{25}.\left(-\frac{17}{6}\right)\)
\(=\frac{7}{25}.\left[\left(-\frac{13}{6}\right)+\left(-\frac{17}{6}\right)\right]\)
\(=\frac{7}{25}.\left(-\frac{30}{6}\right)\)
\(=-\frac{7}{5}\)
b. \(\frac{-4^5.3^5}{2^4.6^4}+2015^0=\frac{\left(-4.3\right)^5}{\left(2.6\right)^4}+1=\frac{-12^5}{12^4}+1=-12+1=-11\)
a) \(\frac{-13.7}{6.25}\)+ \(\frac{-7.17}{25.6}\)=\(\frac{-210}{210}\)=-1
b) \(\frac{-4^4.4.3^4.3}{2^4.3^4.2^4}\)=\(\frac{-2^4.2^4.4.3^4.3}{2^4.3^4.2^4}\)=-12

\(2^3.3-13.2^4+3.8\)
\(2^3.3-13.2.2^3+3.2^3\)
\(2^3.3-26.2^4+3.2^3\)
\(=2^3\left(3-26+3\right)\)
\(=2^3.\left(-20\right)\)
\(=\left(-160\right)\)
\(\frac{25^4.16^3.3^7}{75^4.6^3.8^2}=\frac{5^8.4^6.3^7}{3^4.25^4.2^3.3^3.2^6}=\frac{3^7.2^{12}.5^8}{3^7.5^8.2^9}=2^3=8\)