Final answer:
To solve the expression, we invert the fractions with negative exponents and then perform arithmetic operations. After simplifying the numerator and the denominator, we obtain the solution of 592.
Step-by-step explanation:
To solve the equation ((1/4)⁻³ - (1/3)⁻³) ÷ (1/4)², we'll break it down step by step. First, recall that raising a fraction to a negative exponent inverts the fraction and applies the positive exponent. So ((1/4)⁻³ - (1/3)⁻³) becomes (64 - 27) because (1/4)⁻³ = 4³ = 64 and (1/3)⁻³ = 3³ = 27.
Next, we simplify the denominator, (1/4)², which is just 1/16.
Now we can subtract the numerators (64 - 27), getting 37, and then divide this by the denominator, 1/16, which is the same as multiplying by its reciprocal, 16. Finally, we multiply 37 * 16 which equals 592.
The solution to the expression is therefore 592.