Question

For a ≠ 0, a° is ___​

Answer 1

SOLUTION

TO FILL IN THE BLANK

$\sf{ For \: \: a \ne \: 0 \: \: , \: \: {a}^{0} \: \: is \: }$

EVALUATION

We are aware of the formula on indices that

$\sf{ {a}^{m} \times {a}^{n} = {a}^{m + n} }$

Now take n = 0

So we get from above

$\sf{ {a}^{m} \times {a}^{0} = {a}^{m + 0} }$

$\sf{ \implies {a}^{m} \times {a}^{0} = {a}^{m } }$

$\sf{Dividing \: both \: sides \: by \: \: {a}^{m} \: \: we \: get }$

$\sf{ \implies {a}^{0} = \dfrac{{a}^{m}}{{a}^{m}} }$

$\sf{ \implies {a}^{0} = 1 }$

FINAL ANSWER

$\sf{ For \: \: a \ne \: 0 \: \: , \: \: {a}^{0} = 1}$

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