a.
\(4^{10}\times8^{15}=\left(2^2\right)^{10}\times\left(2^3\right)^{15}=2^{20}\times2^{45}=2^{65}\)
b.
\(4^{15}\times5^{30}=\left(2^2\right)^{15}\times5^{30}=2^{30}\times5^{30}=\left(2\times5\right)^{30}=10^{30}\)
c.
\(\frac{27^{16}}{9^{10}}=\frac{\left(3^3\right)^{16}}{\left(3^2\right)^{10}}=\frac{3^{48}}{3^{20}}=3^{28}\)
d.
\(A=\frac{72^3\times54^2}{108^4}=\frac{\left(8\times9\right)^3\times\left(27\times2\right)^2}{\left(27\times4\right)^4}=\frac{\left(2^3\times3^2\right)^3\times\left(3^3\times2\right)^2}{\left(3^3\times2^2\right)^4}=\frac{2^9\times3^6\times3^6\times2^2}{3^{12}\times2^8}=2^3=8\)
e.
\(B=\frac{3^{10}\times11+3^{10}\times5}{3^9\times2^4}=\frac{3^{10}\times\left(11+5\right)}{3^9\times16}=\frac{3\times16}{16}=3\)
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