Final answer:
To represent the expression ((a²)-2)² as a power of the number a, simplify the expression by expanding the exponent and reorganizing the terms. The final representation as a power of a is a² - 4 + 4/a^2.
Step-by-step explanation:
To represent the expression ((a²)-2)² as a power of the number a, we need to simplify it first. Let's start by expanding the exponent: ((a²)-2)² = (a^4 - 4a² + 4). Now, we can rewrite it as a power of a: (a^4 - 4a² + 4) = a^4/a^2 + (-4a²/a^2) + (4/a^2) = a^(4-2) + (-4a^(2-2)) + 4/a^2 = a² - 4 + 4/a^2. Therefore, the expression ((a²)-2)² can be represented as a power of the number a as a² - 4 + 4/a^2.