Question

Calculati 9^23:[3^44+3^20•27^8+3^60:81^4]-2^20:(2^19+2^19) ;studiati daca 3^7+3^6 este patrat perfect

Answer 1

=9²³:(3⁴⁴+3²⁰·27⁸+3⁶⁰:81⁴)-2²⁰:(2¹⁹+2¹⁹)
=(3²)²³:[3⁴⁴+3²⁰·(3³)⁸+3⁶⁰:(3⁴)⁴]-2²⁰:2¹⁹(1+1)
=3⁴⁶:(3⁴⁴+3²⁰·3²⁴+3⁶⁰:3¹⁶)-2²⁰:2¹⁹·2
=3⁴⁶:(3⁴⁴+3²⁰⁺²⁴+3⁶⁰⁻¹⁶)-2²⁰:2¹⁹⁺¹
=3⁴:(3⁴⁴+3⁴⁴+3⁴⁴)-2²⁰:2²⁰
=3⁴⁶:3⁴⁴(1+1+1)-2²⁰⁻²⁰
=3⁴⁶:3⁴⁴·3-2°
=3⁴⁶:3⁴⁴⁺¹-1
=3⁴⁶:3⁴⁵-1
=3⁴⁶⁻⁴⁵-1
=3-1=2