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a) 9.33.\(\dfrac{1}{81}\) .32 = 32. 33.\(\dfrac{1}{3^4}\) . 32 = 33
b) 4. 25: \(\) (23.\(\dfrac{1}{16}\))= 22. 25: 23. \(\dfrac{1}{2^4}\) = 27: \(\dfrac{1}{2}\) = 27. 2= 28
c) 32. 25. \(\left(\dfrac{2}{3}\right)^2\) = 32. 25. \(\dfrac{2^2}{3^2}\) = 25. 22 = 27
d) \(\left(\dfrac{1}{3}\right)^2\) .\(\dfrac{1}{3}\) . 92 = \(\dfrac{1}{9}.\dfrac{1}{3}\). 92 = \(\dfrac{9}{3}\) = 31
a: \(=3^2\cdot3^3\cdot3^{-4}\cdot3^2=3^{2+3-4+2}=3^3\)
b: \(=2^2\cdot2^5:\left(2^3\cdot\dfrac{1}{2^4}\right)=2^7:\dfrac{1}{2}=2^8\)
c: \(=9\cdot32\cdot\dfrac{4}{9}=128=2^7\)
d: \(=\dfrac{1}{27}\cdot3^4=3^1\)
a) \(3^2.2^5.\left(\frac{2}{3}\right)^2=2^5.\frac{2^2.3^2}{3^2}=2^5.2^2=2^7\)
b) \(\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\frac{1^2.1}{3^2.3}.\left(3^2\right)^2=\frac{1.3^{2.2}}{3^3}=\frac{3^4}{3^3}=3^1\)
a: \(=3^2\cdot3^5:3^4=3^{2+5-4}=3^3\)
b: \(=2^3\cdot2^4:\left(\dfrac{8}{16}\right)=\dfrac{2^7}{2}=2^6\)
c: \(=3^7\cdot3^3=3^{10}\)
d: \(=5^3\cdot5^2\cdot\dfrac{1}{5^4}=5^1\)
a) \(9\cdot3^3\cdot\frac{1}{81}\cdot3^2\)
\(=\frac{3^2\cdot3^3\cdot3^2}{3^4}\)
\(=3^3=27\)
b) \(4\cdot2^5:\left(2^3\cdot\frac{1}{16}\right)\)
\(=\frac{2^2\cdot2^2\cdot2^4}{2^3}\)
\(=2^5=32\)
c) \(3^2\cdot2^5\cdot\left(\frac{2}{3}\right)^2\)
\(=\frac{3^2\cdot2^5\cdot2^4}{3^2}\)
\(=2^9=512\)
d) \(\left(\frac{1}{3}\right)^2\cdot\frac{1}{3}\cdot9^2\)
\(=\frac{1^2\cdot1\cdot3^4}{3^2}\)
\(=3^2=9\)