Problem 110 - Elementary Algebra

Question

\(\left(25-5^{2}\right) \div 10\)

Step-by-Step Solution

Answer

0

Step 1: Calculate the exponent

Evaluate the exponent first. Compute the value of the exponentiation by finding the value of 5 squared: \(5^{2} = 25\)

Step 2: Subtract the exponentiation result

Subtract the result of the exponentiation from 25: \(25 - 25 = 0\)

Step 3: Divide the result by 10

Divide the result from step 2 by 10:\(0 \div 10 = 0\)

Key Concepts

Exponentiation

Exponentiation is a powerful mathematical operation. It's essentially repeated multiplication. For example, when we see something like this: 5², it means we need to multiply 5 by itself once:

• 5² = 5 * 5 = 25

This operation is essential and always takes priority in the order of operations. We call this order the PEMDAS rule: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
In our exercise, we first handle the exponentiation in (25 - 5²). Calculating 5² gives us 25.

Division

Division is one of the basic arithmetic operations that splits a number into equal parts. For example, dividing 10 by 2 means finding how many times 2 fits into 10, which is 5.
When dividing zero by any number, the result is always zero:

• 0 ÷ 10 = 0

In our exercise, after performing the first two steps (exponentiation and subtraction), we end up with 0. The last step is to divide this result by 10, giving us 0.

Subtraction

Subtraction means taking one number away from another. It’s as simple as it sounds, but following the right sequence is crucial. Using the earlier steps, once we've calculated the exponent 5², we need to subtract this from 25.

• First, exponentiation: 5² = 25
• Next, subtraction: 25 - 25 = 0

This step ensures we are correctly simplifying the expression before moving to the final division step.