Question

(a) Write
${2}^{5} \div {2}^{5}$
as a single power if 2.
​

Answer 1

Answer:

2^0

Step-by-step 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.

Answer 2

There are two ways to go about this problem.

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

$\frac{a^n}{a^m}=a^{n-m},a\neq0$.

So,

$\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}$.

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,

$\frac{a}{a}=1, a\neq0$

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

$a^0=1,a\neq0$

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.