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Problem 2

Evaluate the expression: $$3(10+3) \div(8+5)+6 \cdot 4^2$$

Expert verified
The given expression can be simplified step-by-step using the order of operations (PEMDAS). The expression is $3(10 + 3) \div (8 + 5) + 6 \cdot 4^2$ Upon simplification, the expression becomes: $3(13) \div 13 + 6 \cdot 16$ By following PEMDAS, we get: $39 \div 13 + 96$ Finally, we compute the value: $3 + 96 = 99$ Hence, the simplified expression is $$\boxed{99}$$.
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Step 1: Solve expressions inside parentheses first.

We see that there are two sets of parentheses in the expression. We will solve each separately: $3(10+3) \Rightarrow 3(13)$ and $(8+5) \Rightarrow 13$

Step 2: Rewrite expression with simplified terms.

After solving the expressions inside parentheses, we rewrite the overall expression: $3(13) \div 13 + 6 \cdot 4^2$

Step 3: Calculate exponents.

Our expression has one exponent term: $$4^2$$. We will calculate its value: $4^2 = 16$

Step 4: Rewrite expression with calculated exponent.

Now we rewrite the expression with the calculated exponent: $3(13) \div 13 + 6 \cdot 16$

Step 5: Perform multiplication and division from left to right.

Now we perform multiplication and division from left to right: $3 \cdot 13 = 39$ and $6 \cdot 16 = 96$ Leaving us with: $39 \div 13 + 96$ Next, we perform division: $39 \div 13 = 3$

Step 6: Rewrite expression with simplified multiplication and division terms.

Now, we rewrite the expression with the simplified multiplication and division terms: $3 + 96$

Step 7: Perform addition and subtraction from left to right.

Now, we perform addition from left to right: $3 + 96 = 99$ The final result of the expression is 99.

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