Math Problem Statement
Simplify the expression (-3x^4y^3)^4.
Solution
The expression shown in the image is:
Let's simplify this step by step:
Step 1: Apply the power rule
Using the rule , we distribute the exponent to each term inside the parentheses:
Step 2: Simplify each term
- (since raised to an even power becomes positive).
- (using the power of a power rule: ).
- .
Step 3: Combine the results
Final Answer:
Would you like further explanation or related examples? Let me know!
Here are 5 related questions to expand your understanding:
- How does the power rule work for negative bases raised to even and odd powers?
- What happens if there’s an additional variable, such as ?
- How do fractional exponents affect similar expressions?
- Can you explain how to simplify expressions like ?
- How do negative exponents influence the simplification process?
Tip: Always distribute exponents carefully to each part of the expression, especially when there’s a mix of coefficients and variables!
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Math Problem Analysis
Mathematical Concepts
Exponent Rules
Algebraic Simplification
Power of a Product Rule
Power of a Power Rule
Formulas
(a * b)^n = a^n * b^n
(a^m)^n = a^{m*n}
Theorems
Power Rule of Exponents
Suitable Grade Level
Grades 8-10