Math Problem Statement

Bentuk sederhana dari ∛(a⁵.b⁴) adalah ...

Solution

The question is asking for the simplified form of the expression a5b43\sqrt[3]{a^5 \cdot b^4}.

Steps to Simplify:

  1. Break down the cube root: [ \sqrt[3]{a^5 \cdot b^4} = \sqrt[3]{a^5} \cdot \sqrt[3]{b^4} ]

  2. Simplify each term under the cube root:

    • a53=a5/3=a1a2/3\sqrt[3]{a^5} = a^{5/3} = a^1 \cdot a^{2/3}
    • b43=b4/3=b1b1/3\sqrt[3]{b^4} = b^{4/3} = b^1 \cdot b^{1/3}
  3. Combine the simplified terms: [ a^{1} \cdot b^{1} \cdot \sqrt[3]{a^2 \cdot b} = ab \cdot \sqrt[3]{a^2 \cdot b} ]

Final Simplified Form:

The correct simplified form is aba2b3ab \cdot \sqrt[3]{a^2 \cdot b}, which matches Option E.


Do you need more detailed clarification or have any other questions?

Related Questions:

  1. How do you simplify cube roots of higher powers like a73\sqrt[3]{a^7}?
  2. How can we apply this method to expressions with different exponents, such as a8b24\sqrt[4]{a^8 \cdot b^2}?
  3. What is the general rule for simplifying expressions like ambpn\sqrt[n]{a^m \cdot b^p}?
  4. How do cube roots behave when we deal with negative exponents?
  5. How can we solve cube root problems without breaking them down into individual terms?

Tip: Always break down roots into simpler powers and apply the exponent rules carefully!

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Math Problem Analysis

Mathematical Concepts

Exponents
Cube Roots
Algebraic Simplification

Formulas

∛(a^m * b^n) = ∛(a^m) * ∛(b^n)
∛(a^m) = a^(m/3)

Theorems

Exponentiation Theorem
Cube Root Properties

Suitable Grade Level

Grades 9-12