Math Problem Statement
Simplify the following expression in terms of fractional exponents and write it in the form 10 to the power of a x to the power of b.
fifth root of 10 to the power of 4 x end root
Solution
To simplify the given expression, let's follow these steps carefully:
The given expression is:
Step 1: Express the fifth root as a fractional exponent
The -th root of a number can be expressed as a fractional exponent . Therefore:
Step 2: Distribute the fractional exponent
Using the rule , we can split the expression:
Step 3: Simplify the exponents
- For , simplify the exponent: .
- For , the exponent is already simplified.
Thus, the expression becomes:
Final Answer:
The simplified form is:
This is the expression in terms of fractional exponents.
Would you like further explanation on fractional exponents or the rules used here?
Related Questions:
- How do you simplify an expression involving a cube root?
- What are the key properties of fractional exponents?
- How do you distribute fractional exponents over multiplication?
- Can you provide examples of simplifying roots for variables with exponents?
- How do fractional exponents relate to logarithms?
Tip:
When simplifying roots, always express them as fractional exponents first—it makes handling the algebra much more straightforward.
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Math Problem Analysis
Mathematical Concepts
Fractional Exponents
Roots and Radicals
Exponent Rules
Formulas
n-th root of a = a^(1/n)
(a * b)^c = a^c * b^c
Theorems
Properties of Exponents
Distributive Property of Exponents over Multiplication
Suitable Grade Level
Grades 8-10