%5E-2)%5E3-x-(1%2F3)%5E-4-x-3%5E-1-x-1%2F6.jpeg "((-2/3)^-2)^3 X (1/3)^-4 X 3^-1 X 1/6")
Evaluating the Complex Expression:((-2/3)^-2)^3 x (1/3)^-4 x 3^-1 x 1/6
In mathematics, evaluating complex expressions involving exponents, fractions, and multiple operations can be a daunting task. However, by breaking down the expression into smaller parts and applying the correct order of operations, we can simplify the expression and find its value.
Step 1: Evaluating the Exponents
The given expression is: ((-2/3)^-2)^3 x (1/3)^-4 x 3^-1 x 1/6
Let's start by evaluating the exponents:
((-2/3)^-2) = ((-2/3)^2)^-1 = (4/9)^-1 = 9/4
((1/3)^-4) = ((1/3)^4)^-1 = (1/81)^-1 = 81
Step 2: Simplifying the Expression
Now, let's simplify the expression by multiplying the terms:
(9/4)^3 x 81 x 3^-1 x 1/6
Step 3: Evaluating the Powers
Next, let's evaluate the powers:
(9/4)^3 = (729/64)
And:
3^-1 = 1/3
Step 4: Multiplying the Terms
Now, let's multiply the terms:
(729/64) x 81 x (1/3) x (1/6)
Step 5: Simplifying the Final Answer
Finally, let's simplify the final answer:
729/64 x 81/18 = 729/128
Therefore, the value of the given expression is 729/128.
By breaking down the complex expression into smaller parts and applying the correct order of operations, we were able to simplify the expression and find its value.
