Simplify the expression? No calculators

I kinda get it.
Like

81^1/2 you make 2 sqrt 81 than multiply 1

Any other way you know less confusing?

But here the problem I don't get

(7x^1/3)(2x^1/4)

How on earth do you do that?

on your example, what did you do?

81^1/2 is the same as square root (81) = 9

(7x^1/3)(2x^1/4)

First multiply the 7 and 2 together:
14 (x^1/3)(x^1/4)

When multiplying numbers/variables of the same base raised to an exponent, add the exponents.

14 x^(1/3 + 1/4)

Find common denominator:
14 x^(4/12 + 3/12)
14 x^(7/12)

When you multiply two terms, you add the indices.
In this case, the indices are 1/3 and 1/4.
So, the power of x will be 1/3 + 1/4 = 7/12
7 times 2 = 14
answer is 14x^7/12