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What should be the index of x so that the value of x so that it's value will be equal to 1?

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User Giskou
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2 Answers

8 votes

Answer:

In our ordinary division, we are clear about the division of a number by the same number. The quotient is always 1 in such case.

For example:-

Divide 4 by 4.

Here,


(4)/(4) = 1

Now let solve the above examples by using the laws of indices.


(4)/(4) = {4}^(1 - 1) = {4}^(0) = 1

Similarly,


\frac{ {x}^(m) }{ {x}^(m) } = {x}^(m - m) = {x}^(0) = 1

Thus,any base with zero index is equal to 1.

User Harish Sharma
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7.0k points
6 votes

We need to tell the index of x for which x will be 1 , First of all , always remember that index of a number means power of the number or to which power it's raised to, like in , 2 is raised to 3 so 3 is the index. Also we knows an identity i.e


  • {\boxed{\bf{(a^m)/(a^n)=a^(m-n)}}}

Let's put , m = n


{:\implies \quad \sf (a^m)/(a^m)=a^(m-m)}


{:\implies \quad \boxed{\bf{a^(0)=1}}}

Also , you should note that for a = 0 , the given expression becomes 0⁰ ,which is not defined , so the above expression is true only for
{\bf{a\in (-\infty,0)\cup (0,\infty)}}

Now , as we can replace variables , so , if we replace a by x , we get x⁰ = 1 .

Hence , the required index is 0

User Ratislaus
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