Вычислите: а)((〖3^2〗^ 3^5)²)/27³; б)32²/((2^4 )^3•2^6 ).; в)(5^4•10³)/(2^3•〖25〗^2 )

Question

Вычислите: а)((〖3^2〗^ 3^5)²)/27³;
б)32²/((2^4 )^3•2^6 ).;
в)(5^4•10³)/(2^3•〖25〗^2 )

Answer 1

A) (3² * 3⁵)²/27³ = (3²⁺⁵)²/(3³)³ = 3¹⁴/3⁹=3¹⁴⁻⁹=3⁵=243

б) 32²/[(2⁴)³ * 2⁶]=[(2⁵)²] / [2¹² * 2⁶] = 2¹⁰ / 2¹²⁺⁶=2¹⁰ / 2¹⁸ = 1/2⁸ = 1/256

в) (5⁴ * 10³) / (2³ * 25²) = (5⁴ * (2*5)³) / (2³ * (5²)²) =
    =(5⁴ * 2³ * 5³) / (2³ * 5⁴) = (5⁴⁺³ * 2³) / (2³ * 5⁴) =
    = (5⁷ * 2³) / (2³ * 5⁴) = 5⁷⁻⁴=5³=125