Math Problem Statement

(2²×3)³x

Solution

The expression you have is:

(22×3)3×x(2^2 \times 3)^3 \times x

Let's break it down:

  1. First, simplify 222^2: 22=42^2 = 4 So, the expression becomes: (4×3)3×x(4 \times 3)^3 \times x

  2. Now, simplify 4×34 \times 3: 4×3=124 \times 3 = 12 So, the expression becomes: (12)3×x(12)^3 \times x

  3. Next, cube 1212: 123=12×12×12=172812^3 = 12 \times 12 \times 12 = 1728 So the expression simplifies to: 1728×x1728 \times x

Thus, the simplified expression is:

1728x1728x

If you need more explanation or have any further questions, feel free to ask!

Here are 5 related questions to explore further:

  1. How do you simplify expressions with powers and multiplication?
  2. What happens if the variable xx is replaced with a specific number?
  3. How would you simplify (32×4)2×y(3^2 \times 4)^2 \times y?
  4. How do you deal with exponents when multiplying variables?
  5. What is the difference between powers and roots in algebra?

Tip: When simplifying expressions with powers, always handle the operations within parentheses first, then apply exponents, and finally multiply or divide.

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Math Problem Analysis

Mathematical Concepts

Exponents
Simplification
Algebra

Formulas

(a^m × b)^n
a^m = a × a × ... (m times)

Theorems

Power of a product
Exponentiation

Suitable Grade Level

Grades 7-9