What is the value of the expression i⁰× i¹× i²× i³× i⁴?

Solution:

Given expression is an example of multiplication of exponents.

An exponent can be defined as the number of times a quantity is multiplied by itself.

Consider two exponents with the same base, that is, aⁿ and a^m.

Here, the base is a. When the exponents with the same base are multiplied, the powers are added,

i.e., a^m × aⁿ = a^{m+n}

Given that,

i⁰× i¹× i²× i³× i⁴

Here, the base is ‘i’

i⁰× i¹× i²× i³× i⁴

=i^0+1+2+3+4

= i¹⁰

Since we know that i⁴ = 1,

Therefore,

i¹⁰ can be written as ( i⁴)² × i²

= (1) × (-1)

= -1

Alternative method:

We know that,

i⁰ = 1

i¹ = √-1,

i²= -1,

i³ = i² × i = -1 × i = -i

i⁴=1

On substituting all the values, we get

⇒ i⁰× i¹× i²× i³× i⁴

= 1× i× (-1)× -i × 1

= 1 × i²

= 1 × (-1)

= -1

---

What is the value of the expression i⁰× i¹× i²× i³× i⁴?

Summary:

The value of the expression i⁰× i¹× i²× i³× i⁴ is -1.