Math Problem Statement
Solution
Let's break down and simplify the expression in the image step-by-step. The expression is:
Step 1: Apply the exponent to the first fraction
We need to apply the cube () to all the terms in the first fraction:
Simplifying each power:
Thus, the first part simplifies to:
Step 2: Multiply this result by the second fraction
We now have:
We multiply the numerators and the denominators separately:
Numerator:
Denominator:
Step 3: Combine like bases
Now, we combine the powers of each base:
- The terms:
- The terms: remains as it is since there is no in the denominator.
- The terms:
- The terms:
Step 4: Write the final simplified expression
This is the simplified result:
Would you like a detailed explanation of any part? Let me know if you have questions or need further clarifications!
Related Questions:
- How do you simplify fractional exponents like ?
- What are the rules for multiplying powers of the same base?
- How do negative exponents affect a fraction?
- What are common applications of exponent rules in algebraic expressions?
- How can you convert fractional exponents to radical form?
Tip: When working with powers and fractions, always apply exponent rules carefully to both the numerator and denominator.
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Math Problem Analysis
Mathematical Concepts
Exponent Rules
Algebraic Simplification
Fractional Exponents
Formulas
Power of a quotient: \( \left( \frac{a}{b} \right)^n = \frac{a^n}{b^n} \)
Multiplication of exponents: \( a^m \cdot a^n = a^{m+n} \)
Negative exponent rule: \( a^{-n} = \frac{1}{a^n} \)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-12