Math Problem Statement

Which expression is equivalent to 3^4?

Solution

To determine which expression is equivalent to 343^4, let’s analyze each answer choice:

  1. Option A: 333\frac{3^{-3}}{3}

    • Simplify: 333=331=34\frac{3^{-3}}{3} = 3^{-3 - 1} = 3^{-4}, which is not equal to 343^4.
  2. Option B: 334\frac{3}{3^{-4}}

    • Simplify: 334=31+4=35\frac{3}{3^{-4}} = 3^{1 + 4} = 3^5, which is not equal to 343^4.
  3. Option C: 3232\frac{3^2}{3^{-2}}

    • Simplify: 3232=32+2=34\frac{3^2}{3^{-2}} = 3^{2 + 2} = 3^4, which matches 343^4.
  4. Option D: 31033\frac{3^{10}}{3^3}

    • Simplify: 31033=3103=37\frac{3^{10}}{3^3} = 3^{10 - 3} = 3^7, which is not equal to 343^4.

The correct answer is Option C: 3232\frac{3^2}{3^{-2}}, which simplifies to 343^4.

Would you like further details on simplifying exponents?

Here are some related questions:

  1. How do you simplify expressions with negative exponents?
  2. Why does aman=amn\frac{a^m}{a^n} = a^{m-n} work?
  3. What is the rule for multiplying exponents?
  4. How can we convert negative exponents to positive exponents?
  5. What are some common mistakes with exponent rules?

Tip: When dividing powers with the same base, subtract the exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Exponent Rules

Formulas

a^m / a^n = a^(m - n)

Theorems

Exponent Laws

Suitable Grade Level

Grades 8-10