Final answer:
To solve the equation with rational exponents, you must use exponent rules like product of powers, power of a power, and negative exponents to isolate x and solve for it. The question requires algebraic manipulation, including raising both sides to appropriate powers that will remove the fractional exponents.
Step-by-step explanation:
The question concerns solving an equation involving the equality of two expressions with rational exponents: (3x-4)^¹⁄₃ = (16x)^¹⁄⁷. To solve this, one would typically isolate x by raising both sides to powers that would eliminate the fractional exponents, leading to an algebraic equation that can be solved for x.
However, based on the contents provided in the conversation, it seems the student has been working with exponent rules and simplifying expressions rather than solving an equation. This is evident from discussion about rules for multiplying and dividing powers and dealing with negative exponents, which suggests a focus on working with exponents in a general sense rather than solving a particular equation.
The appropriate next steps would be to ensure understanding of exponent rules, such as product of powers, power of a power, and negative exponents, before applying these rules to solve the original equation.