Let's analyze the given expression [tex]\(\frac{b^n}{b^n}\)[/tex].
1. Understanding the Expression:
The problem requires us to simplify the fraction [tex]\(\frac{b^n}{b^n}\)[/tex].
2. Applying the Law of Exponents:
In order to simplify the expression [tex]\(\frac{b^n}{b^n}\)[/tex], we need to apply the properties of exponents. One key property is that when you divide two exponential expressions with the same base, you subtract the exponents:
[tex]\[
\frac{b^m}{b^n} = b^{m-n}
\][/tex]
In our case, both the numerator and the denominator have the same exponent [tex]\(n\)[/tex]. Thus, we can write:
[tex]\[
\frac{b^n}{b^n} = b^{n-n}
\][/tex]
3. Simplifying the Exponent:
Simplifying the exponent [tex]\(n-n\)[/tex] gives:
[tex]\[
n - n = 0
\][/tex]
Therefore, we get:
[tex]\[
b^{n-n} = b^0
\][/tex]
4. Using Another Property of Exponents:
Another important property of exponents tells us that any non-zero number raised to the power of 0 equals 1. Hence:
[tex]\[
b^0 = 1
\][/tex]
As a result, the expression [tex]\(\frac{b^n}{b^n}\)[/tex] simplifies to 1.
Conclusion:
The expression equivalent to [tex]\(\frac{b^n}{b^n}\)[/tex] is always equal to 1, which means none of the given options [tex]\(A, B, C, D\)[/tex] correctly represents [tex]\(\frac{b^n}{b^n}\)[/tex] because the given answer simplifies to 1. However, if [tex]\(b^{n-n}\)[/tex] were presented as one of the options, it would be the correct simplified form in terms of exponents.
