\(2^3. 4^2 . 5^3 \)\(= 8 . 16 . 125 = 16000\)
\(9.3^3.\dfrac{1}{81}.3^3=\left(9.81\right)\left(\dfrac{1}{81}.81\right)=729\)
\(3^2.5^2\left(\dfrac{2}{3}\right)^2=9.25.\dfrac{2^2}{3^2}=9.25.\dfrac{4}{9}=100\)
\(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2=\dfrac{1}{9}.9.\dfrac{1}{3}.9=3\)
\(2^3.4^2.5^3=\left(2^3.5^3\right).4^2=10^3.4^2=1000.16=16000\)
\(9.3^3.\dfrac{1}{81}.3^2=\left(9.\dfrac{1}{81}\right).\left(3^3.3^2\right)=\dfrac{1}{9}.3^5=\dfrac{3^5}{3^2}=3^3=81\)
\(3^2.5^2.\left(\dfrac{2}{3}\right)^2=5^2.\left[3^2.\dfrac{2^2}{3^2}\right]=5^2.2^2=10^2=100\)
\(\left(\dfrac{1}{3}\right)^2.\dfrac{1}{3}.9^2=\left(\dfrac{1}{3}\right)^2.\left(\dfrac{1}{3}.9^2\right)=\dfrac{1}{9}.\dfrac{9^2}{3}=\dfrac{9}{3}=3\)
a) Ta có: \(2^3\cdot4^2\cdot5^3\)
\(=2^3\cdot2^4\cdot5^3\)
\(=2^5\cdot5^3\)
\(=8\cdot125=1000\)
b) Ta có: \(9\cdot3^3\cdot\dfrac{1}{81}\cdot3^2\)
\(=3^5\cdot3^2\cdot\dfrac{1}{3^4}\)
\(=3^7\cdot\dfrac{1}{3^4}\)
\(=\dfrac{3^7}{3^4}=3^3=27\)
c) Ta có: \(3^2\cdot5^2\cdot\left(\dfrac{2}{3}\right)^2\)
\(=\left(3\cdot5\cdot\dfrac{2}{3}\right)^2\)
\(=\left(5\cdot2\right)^2=10^2=100\)
d) Ta có: \(\left(\dfrac{1}{3}\right)^2\cdot\dfrac{1}{3}\cdot9^2\)
\(=\dfrac{1}{9}\cdot\dfrac{1}{3}\cdot9^2\)
\(=\dfrac{1}{27}\cdot81=3\)
