Calculate (6×8)⁴: Evaluating a Product Raised to Fourth Power

To solve the problem of rewriting the expression $(6 \times 8)^4$, we will apply the Power of a Product rule. This rule states that $(a \times b)^n = a^n \times b^n$.

Let's apply this rule to the given expression:

$(6 \times 8)^4$ can be rewritten as $6^4 \times 8^4$ by applying the Power of a Product rule.

Now, let's consider the choices given:

• Choice 1: $6^4 \times 8^4$ - This choice directly corresponds to our rewritten expression using the Power of a Product rule.

• Choice 2: $48^4$ - This represents the product calculated first ($6 \times 8 = 48$) and then raised to the fourth power. This is also a valid representation since $(6 \times 8)^4$ is equivalent to $48^4$.

• Choice 3: $6^4 \times 8$ - This is incorrect because it does not correctly apply the Power of a Product rule.

Therefore, the correct answer according to the given choices is "a' + b' are correct," which indicates the validity of both $6^4 \times 8^4$ and $48^4$ as representations of $(6 \times 8)^4$.