Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Which is the simplified form of [tex]$p^0$[/tex]?

A. [tex]$p$[/tex]
B. [tex]$\frac{1}{p}$[/tex]
C. 0
D. 1


Sagot :

Certainly! Let's simplify the expression [tex]\( p^0 \)[/tex].

In mathematics, any non-zero number raised to the power of 0 is defined to be 1. This is a fundamental principle of exponents.

There are a few ways to understand why this is the case:

1. Definition: By definition, for any non-zero number [tex]\( p \)[/tex], the expression [tex]\( p^n \)[/tex] represents [tex]\( p \)[/tex] multiplied by itself [tex]\( n \)[/tex] times. When [tex]\( n = 0 \)[/tex], we have an empty product of [tex]\( p \)[/tex], and the convention is to define any number to the power of 0 as 1.

2. Exponential Laws: Considering the laws of exponents, specifically the property that [tex]\( p^a \cdot p^b = p^{a+b} \)[/tex], let's set [tex]\( a \)[/tex] and [tex]\( b \)[/tex] to 0. We get:
[tex]\[ p^0 \cdot p^0 = p^{0+0} = p^0. \][/tex]
To maintain consistency, we see that [tex]\( p^0 \)[/tex] must equal 1 because multiplying any number by 1 does not change its value.

3. Sequential Reasoning: Take a series of decreasing exponents, for instance, [tex]\( p^3, p^2, p^1 \)[/tex]. Dividing each by [tex]\( p \)[/tex], we have:
[tex]\[ p^3 = p \cdot p \cdot p, \][/tex]
[tex]\[ p^2 = p \cdot p, \][/tex]
[tex]\[ p^1 = p. \][/tex]
Continuing the pattern, dividing [tex]\( p^1 \)[/tex] by [tex]\( p \)[/tex] once more gives:
[tex]\[ p^0 = \frac{p^1}{p} = \frac{p}{p} = 1. \][/tex]

Therefore, the simplified form of [tex]\( p^0 \)[/tex] is indeed:

[tex]\[ 1 \][/tex]

So, the correct and simplified form of [tex]\( p^0 \)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.