# What is the value of the expression i^{0}× i^{1}× i^{2}× i^{3}× i^{4}?

**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, a^{n} 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} × a^{n} = a^{{m+n}}**

Given that,

i^{0}× i^{1}× i^{2}× i^{3}× i^{4}

Here, the base is ‘i’

i^{0}× i^{1}× i^{2}× i^{3}× i^{4}

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

= i^{10}

Since we know that i^{4} = 1,

Therefore,

i^{10} can be written as ( i^{4})^{2} × i^{2}

= (1) × (-1)

= -1

**Alternative method:**

We know that,

i^{0} = 1

i^{1} = √-1,

i^{2}= -1,

i^{3} = i^{2} × i = -1 × i = -i

i^{4}=1

On substituting all the values, we get

⇒ i^{0}× i^{1}× i^{2}× i^{3}× i^{4}

= 1× i× (-1)× -i × 1

= 1 × i^{2}

= 1 × (-1)

= -1

## What is the value of the expression i^{0}× i^{1}× i^{2}× i^{3}× i^{4}?

**Summary: **

The value of the expression i^{0}× i^{1}× i^{2}× i^{3}× i^{4} is -1.

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