Math Problem Statement

The image contains a math exercise asking to identify expressions with exponents greater than 1 and complete a table of powers for numbers like 8² and 13².

Solution

The image shows a math exercise in Greek. Here's a breakdown of the problems:

Part A: Identify which of the following has an exponent greater than 1.

  1. (α) 7 · 7 · 7
  2. (β) 3 · 3 · 6 · 5 · 5
  3. (δ) 5 · 5 · ... · 5 (19 factors of 5)
  4. (ε) β · β · β · β · β

The task is to express each in exponential form and determine which have exponents greater than 1.

Solutions:

  • (α): 737^3 → Exponent = 3 (greater than 1)
  • (β): 326523^2 \cdot 6 \cdot 5^2 → Both 323^2 and 525^2 have exponents greater than 1.
  • (δ): 5195^{19} → Exponent = 19 (greater than 1)
  • (ε): β5\beta^5 → Exponent = 5 (greater than 1)

Part B: Complete the following table.

The table lists powers and requires base, exponent, and computation. It starts with:

  1. 828^2
  2. 13213^2

You need to calculate:

  • 82=648^2 = 64
  • 132=16913^2 = 169

Would you like further details on these calculations or explanations for each step?

Follow-up Questions:

  1. What is the exponent rule for multiplying numbers with the same base?
  2. How do you simplify products involving different bases, like in (β)?
  3. Can you explain the significance of exponents in real-life applications?
  4. What is the general form of writing numbers in exponential notation?
  5. How does changing the exponent affect the value of the number?

Tip: When simplifying products with multiple terms, first group identical factors to make applying exponents easier!

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication
Algebra

Formulas

Exponential form: a^n where a is the base and n is the exponent
Multiplication of repeated numbers with the same base: a^m * a^n = a^(m+n)

Theorems

Exponentiation: When multiplying the same base, the exponents are added

Suitable Grade Level

Grades 6-8