Final answer:
The product of x⁴/³ times x⁴/³ is x⁸/³, which is x raised to the eight-thirds power.
Step-by-step explanation:
To find the product of x⁴/³ times x⁴/³, we apply the rule for multiplying exponential expressions with the same base, which states that we should add the exponents. We have:
x⁴/³ × x⁴/³ = x⁴/³ + ⁴/³ = x⁸/³
The sum of 4/3 and 4/3 is 8/3, so the result is x⁸/³. This simplifies to x raised to the power of eight-thirds, or the cube root of x raised to the eighth power.