[tex] \begin{align}^3\log 25 \cdot{}^5\log 27 &= {}^3\log 5^2 \cdot{}^5\log 3^3 \\ &= 2\cdot 3\cdot {}^3\log \red5 \cdot{}^{\red{5}}\log 3 \\ &= 6\cdot{}^3\log3 \\ &= 6\cdot 1 \\ &= 6 \end{align} [/tex]
[tex] \begin{align} \dfrac{5^{{}^{25}\log9}}{8^{{}^2\log3}} &= \dfrac{5^{{}^{5^2}\log9}}{2^{3\cdot\:{}^2\log3}} \\ &= \dfrac{5^{{}^{5}\log9^{\frac12}}}{2^{{}^2\log3^3}} \\ &= \dfrac{9^{\frac12}}{3^3} \\ &= \dfrac{3}{3^3} \\ &= \dfrac{1}{9}\end{align} [/tex]
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[tex] \begin{align}^3\log 25 \cdot{}^5\log 27 &= {}^3\log 5^2 \cdot{}^5\log 3^3 \\ &= 2\cdot 3\cdot {}^3\log \red5 \cdot{}^{\red{5}}\log 3 \\ &= 6\cdot{}^3\log3 \\ &= 6\cdot 1 \\ &= 6 \end{align} [/tex]
[tex] \begin{align} \dfrac{5^{{}^{25}\log9}}{8^{{}^2\log3}} &= \dfrac{5^{{}^{5^2}\log9}}{2^{3\cdot\:{}^2\log3}} \\ &= \dfrac{5^{{}^{5}\log9^{\frac12}}}{2^{{}^2\log3^3}} \\ &= \dfrac{9^{\frac12}}{3^3} \\ &= \dfrac{3}{3^3} \\ &= \dfrac{1}{9}\end{align} [/tex]