\(A=\dfrac{-\left(5^2+5.3^2\right)}{5^2\left(5+3^2\right)}\)

\(A=\dfrac{-\left(5\left(5+3^2\right)\right)}{5^2\left(5+3^2\right)}\)

\(A=\dfrac{-5}{5^2}=-\dfrac{1}{5}\)

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1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)

2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)

\(2^x=2.2^8=2^9;x=9\)

4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)

\(\Leftrightarrow3^5.x=3^5.5;x=5\)

\(A=\left[2\cdot3^{15}\cdot3^8-5\cdot3^2\cdot3^{10}\right]\cdot\dfrac{998}{1993006}-1817\)

\(=\left[3^{23}\cdot2-5\cdot3^{12}\right]\cdot\dfrac{998}{1993006}-1817\)

\(=3^{12}\cdot\left[3^{11}\cdot2-5\right]\cdot\dfrac{998}{1993006}-1817\)

\(=\dfrac{1}{1997}\cdot3^{12}\cdot354289-1817\)

\(\simeq94281458.14\)

5.3^x = 5.3⁴

=> x = 4

5.3⁴ = 7.3⁵ - 2.3⁵

       = 3⁵ . (7 - 2)

       = 5. 3⁵

  => 3^x = 3⁵

=> x = 5

{ x² - [ 6² - ( 8² - 9.7)³ - 7.5]³ - 5.3 }³ = 1

{ x² + [ 36 - (64 - 63)³ - 35]³ - 15}³ = 1

[ x² - ( 36 - 1³ - 35 ) - 15 ]³ = 1

[ x² - ( 36 - 1 - 35 ) - 15]³ = 1

[ x² - ( 35 - 35 ) - 15]³ = 1

[ x² - 0 - 15]³ = 1

( x² - 15 )³ = 1

<=> ( x² - 15)³ = 1³

=> x² - 15 = 1

<=> x² = 16

=> x = 4