Question

why something to the zero is equal to 1 (a^0 =1)​

Answer 1

we can write a=a^1,

we also know a/a=1 which is nothing but

a^1/a^1=a^(1-1)=a^0(law of exponents)

Answer 2

let us consider the following example-

$\frac{ {a}^{9} }{ {a}^{7} }$

we know that when we divide two no. with same base and different powers, the powers will subtracted.

it is becomes -

${a}^{9 - 7} = {a}^{2}$

in the same way, we know that

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

$\frac{ {a}^{1} }{ {a}^{1} } = 1$

Solving the LHS we get,

${a}^{1 - 1} = 1 \\ {a}^{0} = 1$