Math Problem Statement

(2^2 · 2^3 - 3^3)^6 ÷ 5^5 + 4 · 3^2 - 5 · 2^3

Solution

Let's analyze and solve the given mathematical expression from the image.

The expression is:

(222333)6:55+432523\left( 2^2 \cdot 2^3 - 3^3 \right)^6 : 5^5 + 4 \cdot 3^2 - 5 \cdot 2^3

Step-by-step solution:

  1. Simplify inside the parentheses: 2223=22+3=25=322^2 \cdot 2^3 = 2^{2+3} = 2^5 = 32 33=273^3 = 27 So, (3227)=5(32 - 27) = 5

  2. Apply the exponentiation: (5)6=15625(5)^6 = 15625

  3. Divide by 555^5: 1562555=156253125=5\frac{15625}{5^5} = \frac{15625}{3125} = 5

  4. Calculate the rest of the terms: 432=49=364 \cdot 3^2 = 4 \cdot 9 = 36 523=58=405 \cdot 2^3 = 5 \cdot 8 = 40

  5. Final expression: 5+3640=15 + 36 - 40 = 1

Final Answer:

The value of the given expression is 11.

Would you like more details or have any questions?


Here are 5 related questions to deepen understanding:

  1. How do we simplify products of powers with the same base?
  2. What is the rule for dividing exponents with the same base?
  3. How do exponent laws apply when simplifying more complex expressions?
  4. What are some shortcuts for calculating higher powers of small numbers?
  5. How do we handle expressions with multiple operations (exponents, multiplication, and division)?

Tip: Always simplify expressions inside parentheses first before applying powers and other operations.

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations
Simplification

Formulas

a^m · a^n = a^(m+n)
Exponentiation: (a)^n
Basic arithmetic: addition, subtraction, multiplication

Theorems

Laws of Exponents
Order of Operations (PEMDAS)

Suitable Grade Level

Grades 9-10