Evaluating Complex Expressions: 500 1/3 x 2 1/3 x (125x3)0
In this article, we will evaluate the complex expression 500 1/3 x 2 1/3 x (125x3)0. This expression involves mixed numbers, multiplication, and exponentiation. To evaluate this expression, we need to follow the order of operations (PEMDAS) and use the correct rules for each operation.
Breaking Down the Expression
Let's break down the expression into smaller parts to make it easier to evaluate:
500 1/3: a mixed number2 1/3: a mixed number(125x3)0: an expression involving multiplication and exponentiation
Evaluating the Mixed Numbers
To evaluate the mixed numbers, we need to convert them to improper fractions:
500 1/3 = 1501/32 1/3 = 7/3
Now we can rewrite the expression using improper fractions:
1501/3 x 7/3 x (125x3)0
Evaluating the Expression Inside the Parentheses
Next, we need to evaluate the expression inside the parentheses:
(125x3)0 = 1250
Now we can rewrite the expression as:
1501/3 x 7/3 x 1250
Multiplying the Fractions
To multiply the fractions, we need to follow the rule for multiplying fractions:
1501/3 x 7/3 = 10507/9
Now we can rewrite the expression as:
10507/9 x 1250
Multiplying the Final Result
Finally, we can multiply the final result:
10507/9 x 1250 = 13080350/9
Final Answer
The final answer is:
13080350/9
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD):
13080350/9 = 1453389
Therefore, the final answer is 1453389.
