Math Problem Statement

Copy and complete the table by writing expressions using exponents and calculating their values for the following repeated factors: 4x4x4x4, 3x3x3x3x3x3, 5x5x5x5x5, and 12x12x12x12.

Solution

In the uploaded image, there is a table asking to write repeated factors as expressions using exponents, and then calculate the values. Here's how we can complete the table:

  1. For 11: 4×4×4×44 \times 4 \times 4 \times 4:

    • Using an exponent: 444^4
    • Value: 44=2564^4 = 256
  2. For 12: 3×3×3×3×3×33 \times 3 \times 3 \times 3 \times 3 \times 3:

    • Using an exponent: 363^6
    • Value: 36=7293^6 = 729
  3. For 13: 5×5×5×5×55 \times 5 \times 5 \times 5 \times 5:

    • Using an exponent: 555^5
    • Value: 55=3,1255^5 = 3,125
  4. For 14: 12×12×12×1212 \times 12 \times 12 \times 12:

    • Using an exponent: 12412^4
    • Value: 124=20,73612^4 = 20,736

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:

  1. How do you simplify expressions involving exponents?
  2. What are the properties of exponents, such as product or power rules?
  3. How can you apply exponents in real-life situations, like calculating compound interest?
  4. How do negative exponents work in expressions?
  5. How do you convert large numbers to scientific notation using exponents?

Tip: When multiplying numbers with the same base, you can add the exponents. For example, xm×xn=xm+nx^m \times x^n = x^{m+n}.

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Math Problem Analysis

Mathematical Concepts

Exponents
Repeated Multiplication
Powers of Numbers

Formulas

a^n = a * a * ... * a (n times)

Theorems

Exponentiation Theorem

Suitable Grade Level

Grade 6-8