Math Problem Statement
Solution
The worksheet you uploaded involves solving problems using the laws of exponents. Here’s a detailed breakdown of each question along with the solutions:
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- Solution:
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- Solution:
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- Solution: Using the law , we get
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- Solution: Using the same law , we get
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- Solution: Using the power of a power rule , we get
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- Solution: Any number raised to the power of 0 equals 1, so
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- Solution: Using the multiplication rule for exponents,
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- Solution: Apply the exponent to both numbers,
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- Solution:
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- Solution: Using the same exponent rule,
Would you like any further details or clarifications on these solutions?
Related Questions:
- What is the general rule for multiplying powers with the same base?
- How does the zero exponent rule apply to different bases?
- Can you explain the power of a product rule with a different example?
- What happens if you multiply two powers with different bases but the same exponent?
- What is the result of , and how does it relate to positive exponents?
Tip:
When multiplying powers with the same base, remember to add the exponents, and when raising a power to another power, you multiply the exponents.
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Math Problem Analysis
Mathematical Concepts
Exponents
Laws of Exponents
Formulas
Product of Powers: a^m × a^n = a^(m+n)
Power of a Power: (a^m)^n = a^(m×n)
Zero Exponent Rule: a^0 = 1
Power of a Product: (ab)^n = a^n × b^n
Theorems
Laws of Exponents
Suitable Grade Level
Grade 6-8
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