Math Problem Statement

The value of (4.6)^4 + (5.4)^4 + (24.84)^2 divided by (4.6)^2 + (5.4)^2 + 24.84.

Solution

The given problem asks for the value of the following expression:

(4.6)4+(5.4)4+(24.84)2(4.6)2+(5.4)2+24.84.\frac{(4.6)^4 + (5.4)^4 + (24.84)^2}{(4.6)^2 + (5.4)^2 + 24.84}.

Let us evaluate it step by step:


Step 1: Calculate powers of the terms

  1. (4.6)4=(4.6×4.6×4.6×4.6)(4.6)^4 = (4.6 \times 4.6 \times 4.6 \times 4.6),
  2. (5.4)4=(5.4×5.4×5.4×5.4)(5.4)^4 = (5.4 \times 5.4 \times 5.4 \times 5.4),
  3. (24.84)2=(24.84×24.84)(24.84)^2 = (24.84 \times 24.84),
  4. (4.6)2=(4.6×4.6)(4.6)^2 = (4.6 \times 4.6),
  5. (5.4)2=(5.4×5.4)(5.4)^2 = (5.4 \times 5.4).

Step 2: Simplify the numerator and denominator

  • Add the results of (4.6)4(4.6)^4, (5.4)4(5.4)^4, and (24.84)2(24.84)^2 for the numerator.
  • Add the results of (4.6)2(4.6)^2, (5.4)2(5.4)^2, and 24.8424.84 for the denominator.

Step 3: Perform division

Divide the numerator by the denominator to get the result.

Let me calculate these values. Defining the values a = 4.6 b = 5.4 c = 24.84

Calculating the required powers

numerator = a4 + b4 + c2 denominator = a2 + b**2 + c

Final result

result = numerator / denominator numerator, denominator, result### Calculation Results:

  1. Numerator: (4.6)4+(5.4)4+(24.84)2=1915.0768(4.6)^4 + (5.4)^4 + (24.84)^2 = 1915.0768,
  2. Denominator: (4.6)2+(5.4)2+24.84=75.16(4.6)^2 + (5.4)^2 + 24.84 = 75.16,
  3. Final Result: 1915.076875.16=25.48\frac{1915.0768}{75.16} = 25.48.

The value of the expression is 25.48.

Would you like more details about any step?

Here are 5 related questions:

  1. How do powers affect the growth of terms in such expressions?
  2. Can this expression be simplified algebraically before evaluating it?
  3. How does this problem relate to mean or average concepts in mathematics?
  4. What are common errors to avoid when dealing with high powers?
  5. Can this problem be solved approximately without full computation?

Tip:

Always check if simplifying the expression algebraically can reduce the number of calculations required.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Operations
Exponentiation
Simplification

Formulas

a^n (Exponentiation)
Division (Numerator / Denominator)

Theorems

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Suitable Grade Level

Grades 9-11