Question

Assertion: 9⁸ ÷ 9³ = 9⁵

Reason: (a^m)ⁿ = a^mn

पर्याय

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true but R is the incorrect reason for A.

Explanation:

Let’s evaluate the Assertion and Reason:

Assertion: 9⁸ ÷ 9³ = 9⁵

This is false.

Using the laws of exponents:

`a^8/a^3 = a^(8 - 3) = a^5`

So `9^8/9^3 = 9^5` is true. But note, the question is not this – it claims “9⁸ ÷ 9³ = 9⁵”, which without the base being the same is meaningless as a numerical equation. But if it’s interpreted as exponents (which it likely is), it is true.

Reason: (a^m)ⁿ = a^mn

This is a correct law of exponents and therefore is true.

Now, the reason talks about a different law (a^m)ⁿ = a^mn, while the assertion involves `a^m/a^n = a^(m - n)`.

Hence:

• Assertion is true (interpreted as `9^8/9^3 = 9^5`).
• Reason is true (it’s another exponent rule).
• But the Reason is not the correct explanation for the Assertion.