Calculate the Product: 9^9 × 8^9 × 2^9 Powers Multiplication

To solve the expression $9^9 \times 8^9 \times 2^9$, we will apply the "Power of a Product" rule in the exponent rules. This rule states that if you have a product of terms all raised to the same exponent, it can be rewritten as the product itself raised to that exponent. The formula is given by:

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

In our problem, we can identify the terms as:

• $a = 9$

• $b = 8$

• $c = 2$

• $n = 9$

Applying the formula, we can convert the product of powers into a single power:

$9^9 \times 8^9 \times 2^9 = (9 \times 8 \times 2)^9$