Math Problem Statement
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.
- (α) 7 · 7 · 7
- (β) 3 · 3 · 6 · 5 · 5
- (δ) 5 · 5 · ... · 5 (19 factors of 5)
- (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): → Exponent = 3 (greater than 1)
- (β): → Both and have exponents greater than 1.
- (δ): → Exponent = 19 (greater than 1)
- (ε): → Exponent = 5 (greater than 1)
Part B: Complete the following table.
The table lists powers and requires base, exponent, and computation. It starts with:
You need to calculate:
Would you like further details on these calculations or explanations for each step?
Follow-up Questions:
- What is the exponent rule for multiplying numbers with the same base?
- How do you simplify products involving different bases, like in (β)?
- Can you explain the significance of exponents in real-life applications?
- What is the general form of writing numbers in exponential notation?
- 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