Final answer:
The expression (3^2)^4 simplifies to 6561 by applying the power of a power rule, which multiplies the exponents together, resulting in 3 to the power of 8.
Step-by-step explanation:
To simplify the expression (3^2)^4, we need to apply the power of a power rule, which states that when we have a power raised to another power, we multiply the exponents. In this case, we have 3 raised to the power of 2, and then this result is raised to the power of 4. Using the rule, we multiply 2 (the exponent inside the parentheses) by 4 (the exponent outside the parentheses), which gives us 32×4 or 38.
Since 32 equals 9, we can also think of the expression as (9)4. Now, we calculate 9 raised to the power of 4. The result of 9×9×9×9 gives us 6561. Therefore, the simplified form of the expression (3^2)^4 is 6561.