Math Problem Statement
(2x^9)^3
Solution
The given image shows the expression . Let's simplify this step by step:
Step-by-step solution:
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Apply the Power of a Power Rule: The general rule applies here. So, for , we multiply the exponents:
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Distribute the exponent to the coefficient: Now apply the exponent to the constant . This follows the same principle:
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Final Expression: Now combine the simplified terms:
Final Answer:
Let me know if you'd like further explanation or have any other questions!
Here are 5 questions based on this solution:
- How does the power rule apply to both numbers and variables in an expression?
- What happens when you have an expression like ?
- How do you simplify using the same rules?
- How would the process change if the expression was instead?
- What is the difference between the power of a product rule and the power of a power rule?
Tip: Always distribute exponents carefully across both coefficients and variables!
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponentiation
Power of a Product Rule
Formulas
(a^m)^n = a^{m * n}
(ab)^n = a^n * b^n
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-10