Question

the index of (-1)^2018 is​

Answer 1

Answer:

negative * negative = positive

therefore when a negative number is multiplyed even number of times the answer will be positive.

positive * negative = negative

(negative * negative) * negative = negative therefore when a negative number us multiplyed odd number of times the answer will be negative

therefore

(-1)^2018=1. [since 2018 is even]

Hope it helps

Answer 2

Index of   (-1)²⁰¹⁸   is 2018

Given  (-1)²⁰¹⁸

To Find : Index

Solution:

xⁿ  is index form  where x  is the base  and n  is the index

(-1)²⁰¹⁸

comparing with xⁿ

x = - 1

Base = - 1

n = 2018

Index = 2018

Index of   (-1)²⁰¹⁸   is 2018

Additional Value :

Now finding value of (-1)²⁰¹⁸

using xᵃᵇ = (xᵃ)ᵇ

2018 = 2 * 1009

= ((-1)²)¹⁰⁰⁹

(-1)² = 1

=  (1)¹⁰⁰⁹

= 1      ( ∵ 1ⁿ  = 1)

Hence (-1)²⁰¹⁸  = 1

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