To simplify the given expression [tex]\(\frac{z^7 y}{z^5 y^4}\)[/tex], we need to follow the rules of algebra, particularly those pertaining to the properties of exponents.
1. Identify and separate the variables in the numerator and the denominator:
[tex]\[
\frac{z^7 y}{z^5 y^4}
\][/tex]
2. Simplify each variable separately by subtracting the exponents of the same base in the denominator from the corresponding exponents in the numerator:
- For the [tex]\(z\)[/tex] terms:
[tex]\[
\frac{z^7}{z^5} = z^{7-5} = z^2
\][/tex]
- For the [tex]\(y\)[/tex] terms:
[tex]\[
\frac{y}{y^4} = y^{1-4} = y^{-3}
\][/tex]
3. Combine the simplified expressions:
[tex]\[
\frac{z^7 y}{z^5 y^4} = z^2 \cdot y^{-3}
\][/tex]
4. Rewrite the expression with positive exponents:
[tex]\[
z^2 \cdot y^{-3} = \frac{z^2}{y^3}
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{z^7 y}{z^5 y^4}\)[/tex] is:
[tex]\[
\frac{z^2}{y^3}
\][/tex]
