Multiply.

(a^2b^2)(a1/3b1/4)

remember, to multiply powers with the same base, we keep the base and add the exponents

(a^2b^2)(a1/3b1/4)
= ????

why do you use ^ to show exponents in the first bracket but not in the second bracket ?
Are they not exponents ?

Sorry, they are exponents! Fractions confuse me, would it be 2/1 + 1/3 and 2/1 + 1/4?

To multiply the given expressions, we can make use of the exponentiation rules.

(a^2b^2)(a1/3b1/4)

First, apply the rule of exponents for multiplying variables with the same base. In this case, "a" is raised to the power of 2 and 1/3, and "b" is raised to the power of 2 and 1/4.

Therefore, we can combine the "a" terms and the "b" terms separately:

(a^2 * a1/3)(b^2 * b1/4)

To simplify the exponent of "a," add the exponents:

a^(2 + 1/3) * b^(2 + 1/4)

Rewrite the exponents with a common denominator:

a^(6/3 + 1/3) * b^(8/4 + 1/4)

Now, simplify the exponents:

a^(7/3) * b^(9/4)

The final result of multiplying the two expressions is:

a^(7/3) * b^(9/4)