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3 votes
(a) Write

{2}^(5) / {2}^(5)
as a single power if 2.


User Massab
by
8.4k points

2 Answers

0 votes

Answer:

2^0

Explanation:

When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.

User NineBerry
by
8.5k points
5 votes

There are two ways to go about this problem.

The first way, the generic way, is to know that,


(a^n)/(a^m)=a^(n-m),a\\eq0.

So,


(2^5)/(2^5)=2^(5-5)=\boxed{2^0}.

The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,


(a)/(a)=1, a\\eq0

And 1 equals to any number raised to the power of zero,


a^0=1,a\\eq0

So we just have to say that the 1 we got is rewritten as some base to the power of zero.

Since our base needs to be 2, we just simply say,


2^0.

Et Viola.

Hope this helps.

User Vashtee
by
7.6k points

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