Problem 94 - Introductory Algebra for College Students

Question

Simplify: \(\left[3\left(12 \div 2^{2}-3\right)^{2}\right]^{2}\) (Section \(1.8,\) Example 8 )

Step-by-Step Solution

Answer

The simplified form of given expression is 0

Step 1: Address the Inner-most Brackets

Start by simplifying the expression within the inner most brackets following the order of operations BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction).\\nNotice that in the expression \(12 \div 2^{2} - 3\), there is an exponent and division that needs to be performed before subtraction.\\nCalculate \(2^{2}\) to get 4, reducing the expression inside the brackets to \(12 \div 4 - 3\).\\nPerform the division next to get 3 - 3. Which simplifies to 0. So, the expression now becomes \(3 \left(0\right)^{2}\).

Step 2: Simplify the Power

Now the zero obtained in the previous step is raised to power 2. That calculates to \(0^{2} = 0\). The expression \(3 \left(0\right)^{2}\) simplifies to \(3 * 0\).

Step 3: Simplify the Remaining Expression

The next step simplifies the multiplication in expression. Which calculates to \(3 * 0 = 0\). But this 0 is inside brackets that is raised to power 2. That gives \(\left[0\right]^{2}\).

Step 4: Simpify the Outer Bracket

The final step is to simplify the power outside the brackets. That calculates to \(0^{2} = 0\).