Math Problem Statement
Solution
It looks like you have uploaded an image with a mathematical expression. The expression is:
[ \frac{3\sqrt[3]{6x^2}}{3\sqrt[3]{5y}} ]
We can simplify this expression step by step.
Step 1: Simplify the constants and the cube roots
The constants in the numerator and denominator are both 3, so they will cancel out:
[ \frac{3\sqrt[3]{6x^2}}{3\sqrt[3]{5y}} = \frac{\sqrt[3]{6x^2}}{\sqrt[3]{5y}} ]
Step 2: Simplify the cube roots
We can combine the cube roots into one:
[ \frac{\sqrt[3]{6x^2}}{\sqrt[3]{5y}} = \sqrt[3]{\frac{6x^2}{5y}} ]
Thus, the simplified expression is:
Would you like to see more steps or explore related concepts? Feel free to ask!
Here are some related questions that could help deepen your understanding:
- How do you simplify expressions with higher roots (like fourth or fifth roots)?
- What is the rule for simplifying expressions with variables under a cube root?
- How do you handle cube roots when there are coefficients?
- What is the difference between cube roots and square roots in terms of simplification?
- Can this simplification be applied to other similar expressions involving cube roots?
Tip: When simplifying expressions with roots, always look for common factors in the numerator and denominator that might cancel out to make the expression simpler.
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Math Problem Analysis
Mathematical Concepts
Radicals
Cube Roots
Algebraic Fractions
Formulas
∛(a) / ∛(b) = ∛(a/b)
Theorems
Properties of Radicals
Suitable Grade Level
Grades 8-10