Problem 112 - Algebra and Trigonometry

Question

Use the order of operations to simplify each expression. $$10^{2}-100 \div 5^{2} \cdot 2-3$$

Step-by-Step Solution

Answer

The final simplified form of the given expression is 89.

Step 1 - Solve the exponent part

Firstly, solve the part of the equation which involves exponents. So, \(10^2 = 100\) and \(5^2 = 25\). Hence, the equation becomes \(100 - 100 \div 25 \cdot 2 - 3\)

Step 2 -Perform the division and multiplication

Once the exponents are solved, proceed to the division and multiplication operations from left to right. Here, \(100 \div 25 = 4\). Then multiply this result by 2 yielding \(4 \cdot 2 = 8\). So, the expression simplifies to \(100 - 8 - 3\)

Step 3 -Perform the subtraction

The final operation is the subtraction. Begin from the left proceeding to the right. Hence, \(100 - 8 = 92\) and then with the subsequent operation \(92 - 3 = 89\)