Math Problem Statement
Solution
The expression provided in the image is:
We are asked to simplify this expression to obtain its positive exponents. Let's proceed step by step:
Step 1: Apply the outer exponent
We can apply the power rule for exponents , which gives us:
Step 2: Apply exponent to each term inside
Now, we apply to each of the factors inside both the numerator and the denominator:
Step 3: Write the new expression
The expression now becomes:
Step 4: Simplify to make all exponents positive
To make all exponents positive, move terms with negative exponents from numerator to denominator (or vice versa):
- goes to the denominator as ,
- moves to the numerator as .
This gives us the simplified expression:
Final Answer:
The expression with all positive exponents is:
Would you like further details or have any questions?
Here are some related questions to deepen your understanding:
- What is the general rule for handling negative exponents?
- How do we simplify expressions with multiple negative exponents?
- Can you explain how the power of a quotient works in terms of exponents?
- How would the simplification change if the outer exponent were positive instead of negative?
- How can we apply these rules to more complex algebraic fractions?
Tip: Always apply exponents step by step, starting from the innermost operations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents
Negative Exponents
Fractional Exponents
Formulas
(a^m / b^n)^p = (a^m)^p / (b^n)^p
a^(-n) = 1/a^n
Theorems
Power of a Quotient Rule
Negative Exponent Rule
Suitable Grade Level
Grades 9-12
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