To simplify the expression [tex]\(\frac{x^6}{x^{16}}\)[/tex], we can use the properties of exponents. Specifically, we use the property that states [tex]\( \frac{a^m}{a^n} = a^{m-n} \)[/tex] when dividing powers with the same base. Here are the steps:
1. Identify the base and the exponents in the given expression [tex]\( \frac{x^6}{x^{16}} \)[/tex]. The base is [tex]\( x \)[/tex], and the exponents are 6 (in the numerator) and 16 (in the denominator).
2. Apply the property of exponents for division:
[tex]\[
\frac{x^6}{x^{16}} = x^{6-16}
\][/tex]
3. Subtract the exponents:
[tex]\[
x^{6-16} = x^{-10}
\][/tex]
4. The simplified form of [tex]\( x^{-10} \)[/tex] can be written as a fraction, using the property that [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]:
[tex]\[
x^{-10} = \frac{1}{x^{10}}
\][/tex]
Therefore, the expression [tex]\(\frac{x^6}{x^{16}}\)[/tex] simplifies completely to [tex]\( \frac{1}{x^{10}} \)[/tex].
