Final answer:
The expression '50 : 25 + 1/5 * 5^3' simplifies to 27 after following the order of operations, calculating the exponent 5^3 as 125, and performing the multiplication and addition.
Step-by-step explanation:
The expression given is 50 : 25 + 1/5 * 5^3. To solve this expression, we should follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is often abbreviated as PEMDAS.
First, let's address the exponent in the term 5^3. Cubing a number means to multiply it by itself three times. Therefore, 5^3 equals 5 x 5 x 5, which is 125.
Next, we perform the multiplication and division from left to right. The given expression, 50 : 25 equals 2 (using ':' as division). Then we multiply 1/5 by 125, which equals 25.
Finally, we add the two results together: 2 + 25 = 27. Therefore, the final answer is 27.