Evaluate 13+((4^3)÷2)*5-17
The question asks you to carry out a series of arithmetic operations involving addition, exponentiation, division, multiplication, and subtraction. You are to evaluate the expression 13 + ((4^3) ÷ 2) * 5 - 17 by following the order of operations, which is commonly remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
$13 + \left(\right. 4^{3} \div 2 \left.\right) \cdot 5 - 17$
Answer
Solution:
Step 1: Break down the expression into simpler components.
- Step 1.1: Calculate the exponentiation of $4$ raised to the power of $3$.
$13 + 4^3 \div 2 \cdot 5 - 17$
$13 + 64 \div 2 \cdot 5 - 17$ - Step 1.2: Perform the division of $64$ by $2$.
$13 + 32 \cdot 5 - 17$ - Step 1.3: Execute the multiplication of $32$ and $5$.
$13 + 160 - 17$
Step 2: Combine the terms by addition and subtraction.
- Step 2.1: Combine $13$ and $160$.
$173 - 17$ - Step 2.2: Deduct $17$ from $173$.
$156$
Knowledge Notes:
The problem involves evaluating a mathematical expression with multiple operations: exponentiation, division, multiplication, addition, and subtraction. The order of operations is crucial to solve such problems correctly. According to the standard mathematical conventions, the order of operations is as follows:
Parentheses (or Brackets) - Perform the operations inside parentheses first.
Exponents - Resolve powers and roots.
Multiplication and Division - These operations are performed from left to right.
Addition and Subtraction - These operations are also performed from left to right.
In LaTeX, mathematical expressions are rendered using specific syntax. For instance, exponents are written using the caret symbol $^$, multiplication by $\cdot$, and division by $\div$. It is important to ensure that the LaTeX code is correctly formatted to display the mathematical expressions accurately.
For the given problem, the expression is simplified by following the order of operations. The exponentiation is performed first, followed by division and multiplication, and finally, addition and subtraction are carried out to arrive at the solution.
