Math Problem Statement

Simplify the expression (3^4 / 3) × 3^2

Solution

The expression in the image is:

(343)×32\left( \frac{3^4}{3} \right) \times 3^2

Let's simplify step by step:

Step 1: Simplify the fraction inside the parentheses

343=341=33\frac{3^4}{3} = 3^{4-1} = 3^3

Step 2: Multiply by 323^2

Now, we multiply the result by 323^2: 33×32=33+2=353^3 \times 3^2 = 3^{3+2} = 3^5

Final Answer:

35=2433^5 = 243

Thus, the expression simplifies to 243243.

Would you like more details or further clarifications?

Here are five related questions you might explore:

  1. What is the general rule for dividing powers of the same base?
  2. How do you simplify expressions with multiple exponents?
  3. What happens when you multiply two powers with the same base?
  4. How can you use exponent rules to simplify more complex expressions?
  5. What is the value of 363^6?

Tip: When working with powers of the same base, remember to subtract exponents when dividing and add exponents when multiplying!

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra
Exponent Rules

Formulas

a^m / a^n = a^(m-n) for division of exponents
a^m × a^n = a^(m+n) for multiplication of exponents

Theorems

Exponent Rules

Suitable Grade Level

Grades 8-10