Fractional Exponent : a^m/n = n √a^m = (n = √a^m), Ex : (√√√√3)^64 = ?

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Fractional Exponent / ভগ্নাংশ সূচক

A fractional exponent is an exponent written in fractional form instead of a whole number. It represents both a power and a root.
ভগ্নাংশ সূচক হৈছে এনে সূচক যি পূৰ্ণসংখ্যাৰ সলনি ভগ্নাংশ আকাৰত লিখা হয়। ই একেলগে ঘাত আৰু মূল (root) বুজায়।

Definition / সংজ্ঞা

a^m/n  = (n√a)^m

Here, a = base , m = power , n = root

Ex: i. 81^1/2= √81= 9  

ii. 27^1/3= 3√27= 3

Important Notes / গুৰুত্বপূর্ণ কথা 

A fractional exponent like a^1/n means the “nth root” of a. You can first take the root and then apply the power, or first apply the power and then take the root. For even roots like square roots, the base should be positive in real numbers.

1. (√√√√3)⁶⁴ = ?

Explanation : 

Easy Trick / সহজ ট্ৰিক

4 square roots means divide the power by 2 four times: 64 ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 4

So,  (√√√√3)⁶⁴ = 3⁴ = 81

2. (√√√3)²⁴  = ?

Explanation : 

Easy Trick / সহজ ট্ৰিক

3 square roots mean divide the power by 2 three times:

24 ÷ 2 ÷ 2 ÷ 2 = 3

so, (√√√3)²⁴= 3³ = 27

Ans / উত্তৰ: 27