Math Problem Statement
Simplify the expression \( \frac{\sqrt[3]{24^4}}{24} \)
Solution
It looks like the expression in the image is:
Let me simplify this step by step:
Step 1: Simplifying the numerator
The numerator is , which is the cube root of . This can be rewritten as:
Step 2: The full expression
Now, the expression becomes:
Since , we can rewrite this as:
Step 3: Simplifying the result
The final result is:
So, the simplified form of the expression is:
Would you like more details or have any questions?
Here are five related questions to explore further:
- What is the cube root of 24 approximated to two decimal places?
- How do you simplify expressions involving roots and exponents?
- What is the general rule for dividing powers with the same base?
- Can the expression be simplified further into a decimal?
- How would you express ?
Tip: When dealing with roots and exponents, converting expressions into powers often makes simplification easier.
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Math Problem Analysis
Mathematical Concepts
Exponents
Roots
Simplification of Expressions
Formulas
Cube root of a power: \( \sqrt[3]{a^b} = a^{\frac{b}{3}} \)
Division of powers with the same base: \( \frac{a^m}{a^n} = a^{m-n} \)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-12