Math Problem Statement
Solution
Let's simplify the given expression step by step. The expression is:
Step 1: Simplifying the first term
- since 5 is the square root of 25.
- since .
Step 2: Simplifying the second term
- First, calculate the fourth root: (since ) and (since ).
- The expression becomes , which is the reciprocal: .
Step 3: Simplifying the third term
- First, take the cube root: and .
- The expression becomes .
- Now square this: .
- The reciprocal is: .
Step 4: Adding all terms
Now sum the results:
- Convert all fractions to have a common denominator of 16:
- Adding the fractions:
Thus, the simplified expression is:
Would you like more details or explanations on any step? Here are some related questions to explore further:
- How do you find the reciprocal of a fraction raised to a negative exponent?
- What is the cube root of a number, and how do you calculate it?
- How can you add fractions with different denominators efficiently?
- How do you evaluate fractional exponents like ?
- Why does raising a fraction to a negative exponent involve taking the reciprocal?
Tip: When simplifying roots and exponents, it's often helpful to rewrite the terms in fractional form for easier manipulation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radicals
Exponents
Fractions
Formulas
√a (Square Root)
∛a (Cube Root)
(a/b)^n
Reciprocal of a fraction raised to a negative power
Theorems
Laws of exponents
Radical simplification
Suitable Grade Level
Grades 9-10
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