Calculate (2×5×4)^7: Evaluating a Product Raised to a Power

The problem requires simplifying the expression $(2\times5\times4)^7$ using the power of a product rule. According to the exponent rules, specifically the power of a product rule, we know that:

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

This means when we have a product raised to an exponent, each factor in the product is raised to that exponent. So let's apply this rule to the given expression:

• First, identify the terms inside the parentheses: 2, 5, and 4.

• Next, apply the exponent 7 to each term:

  • $2^7$ – The first term 2 is raised to the power of 7.

  • $5^7$ – The second term 5 is raised to the power of 7.

  • $4^7$ – The third term 4 is raised to the power of 7.

Therefore, the expression $(2\times5\times4)^7$ simplifies to:

$2^7\times5^7\times4^7$