Question

Evaluate : (1296) to the power ¼ ×(1296) to the power ½.​

Answer 1

To evaluate :-

$\displaystyle{\sf{1296^\frac{1}{4}\times 1296^\frac{1}{2} }}$

Simplifying :-

$\sf{=[(36)^2]^\frac{1}{4} \times [(36)^2]^\frac{1}{2} }\\\\\sf{=36^\frac{2}{4} \times 36^\frac{2}{2} }\\\\\sf{=36^\frac{1}{2} \times 36^1 }\\\\\sf{=36 ^{\frac{1}{2}+1 }}\\\\\sf{=36^{\frac{3}{2} }}\\\\\sf{=[(6)^2]^\frac{3}{2} }\\\\\sf{=6^{2 \times \frac{3}{2} }}\\\\\sf{=6^3}\\\\\large\boxed{\sf{=216}}$