What expressions are equivalent to 2 to the power of 6
A. 6x6x6x6x6x6
B.2x2x2x2x2x2
C.2×6
D.4×16
E.12×12
F.8×8
The Correct Answer and Explanation is :
The expression that is equivalent to (2^6) (2 to the power of 6) is B. (2 \times 2 \times 2 \times 2 \times 2 \times 2).
Breakdown:
- (2^6) means multiplying 2 by itself six times:
[
2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64
]
This matches option B, where 2 is multiplied six times to give a result of 64.
Why Other Options Are Incorrect:
- A. (6 \times 6 \times 6 \times 6 \times 6 \times 6): This represents (6^6), not (2^6). Multiplying six by itself six times results in a much larger number:
[
6 \times 6 \times 6 \times 6 \times 6 \times 6 = 46656
]
This is not equivalent to 64, so it’s incorrect. - C. (2 \times 6): This simplifies to 12, not 64. It’s just a basic multiplication and doesn’t reflect repeated multiplication as in (2^6).
- D. (4 \times 16): While this is closer, it equals 64 by coincidence, but it doesn’t express (2^6). Instead, it represents (4^1 \times 16^1), which isn’t the correct breakdown for (2^6).
- E. (12 \times 12): This equals 144, which is much larger than 64 and doesn’t involve base 2.
- F. (8 \times 8): This equals 64, but like option D, it’s coincidental. (8 \times 8) results from multiplying powers of 2 (since (8 = 2^3)), but it doesn’t directly reflect (2^6).
Thus, B. (2 \times 2 \times 2 \times 2 \times 2 \times 2) is the only option that properly represents (2^6).