Final answer:
The expression (8^2)^9 simplifies to 8^18 by multiplying the exponents, which means the correct answer is 8 to the power of 18, not 8 to the power of 11 as stated in the question.
Step-by-step explanation:
When simplifying the expression (82)9, we need to apply the rule that states when you raise a power to a power, you multiply the exponents. Applying this rule to our expression, we get 82×9, which simplifies to 818, not 811 as incorrectly stated in the question. This is because we multiply the exponent 2 (from 82) by the exponent 9, giving us an exponent of 18.
Just like in other examples of exponentiation, such as squaring of exponentials where we multiply the exponent by 2, the same multiplication rule applies for any exponents when powers are raised to another power.
Therefore, the correct simplified expression is 818.