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1)
a. \(\left(3x^2-50\right)^2=5^4\)
\(\Leftrightarrow3x^4-50=625\)
\(\Leftrightarrow3x^4=675\)
\(\Leftrightarrow x^4=225\)
\(\Leftrightarrow x=\sqrt{15}\)
2)
a. \(\frac{\left(3^4-3^3\right)^4}{27^3}=\frac{3^{16}-3^{12}}{\left(3^3\right)^3}=\frac{3^{12}.3^4-3^{12}}{3^9}=\frac{3^{12}\left(3^4-1\right)}{3^9}\)
\(=\frac{3^{12}.80}{3^9}=3^3.80=27.80=2160\)
b. \(\frac{25^3}{\left(5^5-5^3\right)^2}=\frac{\left(5^2\right)^3}{5^{10}-5^6}=\frac{5^6}{5^6.5^4-5^6}=\frac{5^6}{5^6\left(5^4-1\right)}\)
\(=\frac{5^6}{5^6.624}=\frac{1}{624}\)
(1/3)50. (-9)25 - 2/3 : 4
= (1/3)50 . [(-3)2]25 - 2/3 . 1/4
= (1/3)50.(-3)50- 1/6
= (1/3 . -3 )50 - 1/6
= (-1)50- 1/6
= 1 - 1/6
= 5/6
theo đề ta có
=\(\left(\frac{1}{3^{ }}\right)^{50}.\left(-9\right)^{25}-\frac{2}{3}.\frac{1}{4}\)
=\(\left(\frac{1}{3}\right)^{50}.\left(\frac{1}{3}\right)^{25}.\left(-27\right)^{25}-\frac{1}{6}\)
=\(\left(\frac{1}{3}\right)^{50+25}.\)
=(1\3)^50.(-3^20)^25-1\6
=(1\3)^50.(-3)^50-1\6
=(-1)^50-1\6
=1-1\6
=5\6
a) \(\left[\frac{1}{3}\right]^{50}.\left(-9\right)^{25}-\frac{2}{3}:4\)
\(\Rightarrow\frac{1}{3^{50}}.\left(-9\right)^{25}-\frac{2}{3}.\frac{1}{4}\)
\(\Rightarrow\frac{\left(-9\right)}{9^{25}}-\frac{1}{6}\)
\(\Rightarrow1-\frac{1}{6}\)
\(\Rightarrow\frac{6}{6}-\frac{1}{6}=\frac{5}{6}\)
Vậy = 5/6
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\(=-\left(\dfrac{1}{3}\right)^{50}\cdot3^{50}-\dfrac{2}{3}\cdot\dfrac{1}{4}=-1-\dfrac{1}{6}=-\dfrac{7}{6}\)