Question

Which power of 8 is equal to 2⁶?

Options

• 3

• 2

• 1

• 4

Answer 1

2

Explanation:

Let power of 8 be x.

According to the question,

8^x = 2⁶

⇒ (2³)^x = 2⁶  ...[∵ 8 = 2 × 2 × 2 = 2³]

⇒ 2^3x = 2⁶  ...[∵ (a^m)ⁿ = a^m × ⁿ]

Since, base are equal, then by equating their exponents, we get

3x = 6

⇒ `(3x)/3 = 6/3`  ...[Dividing both sides by 3]

⇒ x = 2

Hence, the power of 8 is 2, which is equal to 2⁶.