Simplify:
4^1/3 (2^1/3 × 3^1/2) ÷ 9^1/4

The correct answer is: Simplifying the given expression, we get- 2.

Hint:-
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as aⁿ, where a is called the base and n is its power/ exponent.
aⁿ = a × a × ... × a             n times.
Step-by-step solution:-
4^1/3 (2^1/3 × 3^1/2) ÷ 9^1/4
= (2²)^1/3 (2^1/3 × 3^1/2) × 1/(3²)^1/4 …......................................................... (Taking reciprocal)
= 2^2/3 × 2^1/3 × 3^1/2 × 1/3^2/4 …................................................................ [(bⁿ)^m = b^nm]
= 2^2/3 × 2^1/3 × 3^1/2 × 1/3^1/2
= 2^2/3+1/3 × 3^1/2-1/2 ............................................................................... (an *⋅am = an+m & an/am = an-m)
= 2¹ × 3⁰
= 2 × 1 ................................................................................................. (b1 = b & b0 = 1)
= 2.
Final Answer:-
∴ Simplifying the given expression, we get- 2.