Evaluating Arithmetic Expression Step-by-Step
The problem asks to evaluate the expression: $\frac{\{(13)^3 - 4^3\}}{13 - 8 \div 2} \div 8 - \{2 + 6 \times 9\}$. We need to follow the order of operations (BODMAS/PEMDAS: Brackets/Parentheses, Orders/Exponents, Division and Multiplication, Addition and Subtraction).
Numerator Calculation: Exponents and Subtraction
- Calculate the powers: $13^3 = 2197$ and $4^3 = 64$.
- Subtract the results: $2197 - 64 = 2133$.
Denominator Calculation: Division and Subtraction
- Perform division first: $8 \div 2 = 4$.
- Perform subtraction: $13 - 4 = 9$.
First Fraction Simplification
- Divide the numerator by the denominator: $\frac{2133}{9} = 237$.
Brackets Calculation: Multiplication and Addition
- Perform multiplication inside the braces: $6 \times 9 = 54$.
- Perform addition: $2 + 54 = 56$.
Combining Operations: Division and Final Subtraction
- The expression is now: $237 \div 8 - 56$.
- Perform the division: $237 \div 8 = \frac{237}{8}$.
- Convert 56 to a fraction with denominator 8: $56 = \frac{56 \times 8}{8} = \frac{448}{8}$.
- Perform the final subtraction: $\frac{237}{8} - \frac{448}{8} = \frac{237 - 448}{8}$.
- Calculate the final result: $\frac{-211}{8}$.
The final value of the expression is $-\frac{211}{8}$.
Similar Questions
What will the value of the following expression be?
$\left(\frac{6+3}{3}\right) - 5 \times (4+5)$
- What is the value of the following expression?
$\frac{\sqrt{225}}{14} \times \frac{\sqrt{196}}{22} \times \frac{\sqrt{484}}{15}$ - The value of $\frac{(5.4)^3 - 0.064}{(5.4)^2 + 2.16 + 0.16}$ is:
- The value of $\sqrt{10 + \sqrt{221 + \sqrt{12 + \sqrt{16}}}}$ is:
- Solve the following.
$(1 + \frac{1}{x})(1 + \frac{1}{x+1})(1 + \frac{1}{x+2})(1 + \frac{1}{x+3}) = ?$ - The value of $\sqrt{0.04} + \sqrt{1.44} + \sqrt{1.69} + \sqrt{0.0009}$ is:
- The value of $\frac{32 \div 4 - 5 \times 8 \div 3}{5 \times 3 - \{6 + 3\}}$ is:
- What is the value of $x$, if $-3 \times \sqrt{196} + \sqrt{x} = 8 \times 3 - 2$?
- What is the value of $\sqrt{\frac{1.21 \times 0.9}{1.1 \times 0.11}}$?
- What is the value of the following expression?
$\frac{81}{7} \times \frac{21}{3} - 4\frac{2}{3} \div \frac{7}{9} \times \frac{121}{6}$
Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
