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Why is 2 to the power 0 is 1?

Updated: 9/23/2023
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11y ago

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Any number, raised to the power 0 is 1.

This comes from the index law: ax* ay= ax+y

Let y = 0 and you have ax* a0= ax+0

But x+0 = x so the right hand side is ax.


That means ax* a0= ax


Since this is true for all a, a0must be the multiplicative identity = 1.




Any number, raised to the power 0 is 1.

This comes from the index law: ax* ay= ax+y

Let y = 0 and you have ax* a0= ax+0

But x+0 = x so the right hand side is ax.


That means ax* a0= ax


Since this is true for all a, a0must be the multiplicative identity = 1.




Any number, raised to the power 0 is 1.

This comes from the index law: ax* ay= ax+y

Let y = 0 and you have ax* a0= ax+0

But x+0 = x so the right hand side is ax.


That means ax* a0= ax


Since this is true for all a, a0must be the multiplicative identity = 1.




Any number, raised to the power 0 is 1.

This comes from the index law: ax* ay= ax+y

Let y = 0 and you have ax* a0= ax+0

But x+0 = x so the right hand side is ax.


That means ax* a0= ax


Since this is true for all a, a0must be the multiplicative identity = 1.


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Wiki User

11y ago
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User Avatar

Wiki User

11y ago

Any number, raised to the power 0 is 1.

This comes from the index law: ax* ay= ax+y

Let y = 0 and you have ax* a0= ax+0

But x+0 = x so the right hand side is ax.


That means ax* a0= ax


Since this is true for all a, a0must be the multiplicative identity = 1.


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