Evaluate the Expression: 7¹¹ × 3¹¹ × 8 Using Exponent Properties

To solve the given expression, we need to apply the power of a product rule from exponent rules. This rule states that when you have a product of numbers raised to the same power, you can combine them under one exponent. The formula is as follows:

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

In our problem, we are given:
$7^{11}\times3^{11}\times8$

We notice that $7^{11}$ and $3^{11}$ are raised to the same power, 11. Therefore, according to the power of a product rule, we can combine them:

• Identify the terms with the same power: $7^{11}$ and $3^{11}$.

• Combine the terms under a single exponent: $(7 \times 3)^{11}$.

This means:

$7^{11}\times3^{11} = (7\times3)^{11}$

Thus, our simplified expression now looks like this:

$(7\times3)^{11}\times8$