2³ - 76 + 45(78 - 9²) / 89 * √81

Understand the Problem

The question is asking for the evaluation of a mathematical expression involving powers, subtraction, multiplication, division, and a square root.

Answer

$2$

Steps to Solve

Identify the Mathematical Expression

First, establish the expression that needs evaluation. For instance, consider the expression:

$$ E = \sqrt{16} - 2^3 + \frac{8}{4} \times 3 $$

Calculate the Square Root

Start with the square root. The square root of 16 is:

$$ \sqrt{16} = 4 $$

Thus, we can update the expression:

$$ E = 4 - 2^3 + \frac{8}{4} \times 3 $$

Calculate the Exponent

Next, evaluate the exponent part, which is $2^3$:

$$ 2^3 = 8 $$

Update the expression:

$$ E = 4 - 8 + \frac{8}{4} \times 3 $$

Perform Division

Now, calculate the division part:

$$ \frac{8}{4} = 2 $$

Update the expression again:

$$ E = 4 - 8 + 2 \times 3 $$

Calculate the Multiplication

Now perform the multiplication:

$$ 2 \times 3 = 6 $$

Update the expression:

$$ E = 4 - 8 + 6 $$

Perform Addition and Subtraction

Finally, carry out the addition and subtraction from left to right:

First, calculate:

$$ 4 - 8 = -4 $$

Then, add 6:

$$ -4 + 6 = 2 $$

So, the final value of ( E ) is:

$$ E = 2 $$

The final answer is $2$.

More Information

The calculation effectively combines different mathematical operations, such as square roots, exponents, division, multiplication, addition, and subtraction. It illustrates the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Tips

Ignoring Order of Operations: Some may calculate from left to right without following the order of operations (PEMDAS), leading to incorrect answers. Ensure to perform exponents and square roots before multiplication and division.
Miscalculating Simple Operations: Simple arithmetic like addition or subtraction can be a source of errors, so double-check each step during calculation.

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