Math Problem Statement
Solution
The expression you uploaded is:
Let’s simplify the expression step by step.
Step 1: Simplify the expression inside the parentheses.
We have:
-
For the powers of 5:
-
For the powers of 3:
Now, the expression becomes:
Step 2: Apply the outer exponent of .
We now have the following expression:
Using the power of a product rule:
Step 3: Final expression.
The simplified form of the expression is:
This is the final answer.
Would you like to explore further details or have any questions?
Here are 5 related questions:
- How do we handle negative exponents in simplification?
- What is the product of powers rule in exponents?
- How can we simplify expressions with different bases?
- What are the steps to simplify more complex fractions with exponents?
- How do we apply exponentiation to a product?
Tip: Remember that when dividing powers with the same base, subtract the exponents!
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Math Problem Analysis
Mathematical Concepts
Exponents
Simplification
Power of a Product
Negative Exponents
Formulas
Power of a product rule: \((a^m \cdot b^n)^p = a^{mp} \cdot b^{np}\)
Negative exponent rule: \(a^{-n} = \frac{1}{a^n}\)
Division of exponents: \(\frac{a^m}{a^n} = a^{m-n}\)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-11
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