Final answer:
The result of 6⋅3^(-2) - 3^4⋅9 + 4^0 is -242.
Step-by-step explanation:
To solve the expression 6⋅3^(-2) - 3^4⋅9 + 4^0, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right). In this case, we start by evaluating the exponents:
6⋅3^(-2) becomes 6⋅(1/3)^2 = 6⋅1/9 = 6/9 = 2/3
Next, we evaluate 3^4⋅9, which is equal to 81⋅9 = 729.
Finally, we substitute 4^0 for 1 (any number raised to the power of 0 is equal to 1).
Putting it all together, the expression becomes 2/3 - 729 + 1 = 2/3 - 728.
So, the answer is -726/3, which simplifies to -242.