To simplify the expression [tex]\(\frac{x^{41}}{y^{15}} \cdot \frac{y^{15}}{x^{41}}\)[/tex], follow these steps:
1. Rewrite the Expression:
We start with the expression:
[tex]\[
\frac{x^{41}}{y^{15}} \cdot \frac{y^{15}}{x^{41}}
\][/tex]
2. Combine Fractions:
We can combine the two fractions into a single fraction:
[tex]\[
\frac{x^{41} \cdot y^{15}}{y^{15} \cdot x^{41}}
\][/tex]
3. Simplify the Numerator and Denominator:
Notice that in both the numerator and denominator, we have the same terms [tex]\(x^{41}\)[/tex] and [tex]\(y^{15}\)[/tex]:
[tex]\[
\frac{x^{41} \cdot y^{15}}{y^{15} \cdot x^{41}}
\][/tex]
4. Cancel Out Like Terms:
The [tex]\(x^{41}\)[/tex] term in the numerator cancels with the [tex]\(x^{41}\)[/tex] term in the denominator, and similarly, the [tex]\(y^{15}\)[/tex] term in the numerator cancels with the [tex]\(y^{15}\)[/tex] term in the denominator:
[tex]\[
\frac{1}{1}
\][/tex]
5. Simplified Result:
After canceling out the like terms, the expression simplifies to:
[tex]\[
1
\][/tex]
Thus, the simplified expression is:
[tex]\[
\frac{x^{41}}{y^{15}} \cdot \frac{y^{15}}{x^{41}} = 1
\][/tex]
