Calculate (2×6×8)⁴: Evaluating a Power of Multiple Numbers

Choose the expression that corresponds to the following:

$\left(2\times6\times8\right)^4=$

To solve the question, we need to apply the power of a product rule from exponents. This rule states that when a product is raised to an exponent, we can apply the exponent to each factor within the product individually. Mathematically, the rule is expressed as:

$(a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n$.

Now, we identify the components in the given expression:

• The expression inside the parentheses is $2 \times 6 \times 8$.
• The exponent applied to this product is $4$.

Applying the exponent to each factor gives us:

• Apply the exponent 4 to the factor 2: $2^4$.
• Apply the exponent 4 to the factor 6: $6^4$.
• Apply the exponent 4 to the factor 8: $8^4$.

Therefore, the expression $(2 \times 6 \times 8)^4$ is transformed into:

$2^4 \times 6^4 \times 8^4$.

This matches the correct answer provided: $2^4 \times 6^4 \times 8^4$.