Daraja va uning xossalari, darajali ifodalar bo‘yicha savol

Berilgan $2^{x}=a$, $3^{x}=b$, $5^{x}=c$ tenglamalarini yodda tutib, $120$ning asosli ko‘paytmasini ajratamiz: \[ 120 = 2^{3}\cdot 3^{1}\cdot 5^{1}. \] Endi $120^{x}$ ni har bir asosning $x$‑darajaga ko‘tarilgan ko‘rinishida yozamiz: \[ 120^{x} = (2^{3}\cdot 3^{1}\cdot 5^{1})^{x}=2^{3x}\,3^{x}\,5^{x}. \] $2^{x}=a$, $3^{x}=b$, $5^{x}=c$ bo‘lgani uchun $2^{3x}=(2^{x})^{3}=a^{3}$. Shuning uchun \[ 120^{x}=a^{3}\,b\,c. \] Demak, $120^{x}$ ni $a$, $b$, $c$ orqali ifodalash natijasi \(\displaystyle a^{3}bc\), ya’ni **C** variantidir.