Solve (12×5×4)^10: Evaluating a Product Raised to the Tenth Power

To solve the expression $\left(12 \times 5 \times 4\right)^{10}$, we apply the rule of exponents known as the "Power of a Product". This rule states that when you have a product inside a power, you can apply the exponent to each factor in the product separately. This can be expressed by the formula:

$(a \times b \times c)^n = a^n \times b^n \times c^n$

In the given expression, the base is the product $12 \times 5 \times 4$ and the exponent is $10$.

Therefore, according to the power of a product rule, the expression can be rewritten by raising each individual base to the power of $10$:

• Raise 12 to the 10th power: $12^{10}$

• Raise 5 to the 10th power: $5^{10}$

• Raise 4 to the 10th power: $4^{10}$

Thus, the expression $\left(12 \times 5 \times 4\right)^{10}$ simplifies to:

$12^{10} \times 5^{10} \times 4^{10}$

This shows the application of the Power of a Product rule for exponents by distributing the 10th power to each term within the parentheses.