Question

Assertion: 7³ × 7⁴ = 7¹²

Reason: a^m × aⁿ = a^{m + n} where a ≠ 0

Options

• 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

A is false but R is true.

Explanation:

Let’s break down the assertion and the reason:

Assertion:

7³ × 7⁴

= 7¹²

Using the property of exponents a^m × aⁿ = a^{m + n}, we have:

7³ × 7⁴

= 7³⁺⁴

= 7⁷

So, the assertion 7³ × 7⁴ = 7¹² is false because the correct answer is 7⁷.

Reason:

a^m × aⁿ = a^{m + n} where a ≠ 0

This is a true property of exponents.