Assertion : We know that
`9div3=3` and `9^(3)div3^(3)=27`
`8div2=4` and `8^(3)div2^(3)=64`
Reason : If a divides b, then `a^(3)` divides `b^(3)`.

Options

A. If both asseration and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assartion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the assertion and reason provided in the question, we will break it down step by step.

### Step 1: Understanding the Assertion
The assertion states:
1. \( 9 \div 3 = 3 \) and \( 9^3 \div 3^3 = 27 \)
2. \( 8 \div 2 = 4 \) and \( 8^3 \div 2^3 = 64 \)

**Verification:**
- For \( 9 \div 3 = 3 \):
- This is true as \( 9 \div 3 = 3 \).

- For \( 9^3 \div 3^3 = 27 \):
- Calculate \( 9^3 = 729 \) and \( 3^3 = 27 \).
- Now, \( 729 \div 27 = 27 \), which is true.

- For \( 8 \div 2 = 4 \):
- This is also true as \( 8 \div 2 = 4 \).

- For \( 8^3 \div 2^3 = 64 \):
- Calculate \( 8^3 = 512 \) and \( 2^3 = 8 \).
- Now, \( 512 \div 8 = 64 \), which is true.

**Conclusion for Assertion:**
Both parts of the assertion are true.

### Step 2: Understanding the Reason
The reason states:
"If \( a \) divides \( b \), then \( a^3 \) divides \( b^3 \)."

**Verification:**
- Let \( a \) divide \( b \). This means there exists an integer \( k \) such that:
\[ b = a \times k \]
- Now, cubing both sides:
\[ b^3 = (a \times k)^3 = a^3 \times k^3 \]
- This shows that \( b^3 \) is divisible by \( a^3 \).

**Conclusion for Reason:**
The reason is also true as it correctly explains the relationship between divisibility and cubing.

### Final Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

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