Question

I need help on this question I’m confused I think a &b are the same and c &d are different but I’m not to sure !

Answer 1

Answer:  They're all the same

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Reason:

$2^6$ means we have 6 copies of "2" multiplied out as shown in choice B. That explains how A and B are the same, and we can say

$2^6 = (2*2*2)*(2*2*2)$

The parenthesis are optional, but I find they're handy to count the '2's easier.

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Now notice that

$2^3 = 2*2*2$

So,

$2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2^3)*(2^3)\\\\2^6 = (2^3)^2$

The last step is possible because we have two copies of $2^3$ multiplied together.

This shows that choice C is equivalent to A and B.

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Lastly,

$2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2*2)*(2*2)*(2*2)\\\\2^6 = (2^2)*(2^2)*(2^2)\\\\2^6 = (2^2)^3$

The jump to the last step is possible because we have three copies of $2^2$ multiplied together.

This shows choice D is equivalent to the others.

All four expressions are the same.

They represent different ways to say the same number. That number being 64.