Certainly! Let's simplify the expression step by step.
We start with the expression:
[tex]\[
\frac{x^2 y z \times x^3 z^5}{x^5 y z^4}
\][/tex]
1. Combine the terms in the numerator:
- The terms in the numerator are [tex]\(x^2\)[/tex], [tex]\(y\)[/tex], [tex]\(z\)[/tex], [tex]\(x^3\)[/tex], and [tex]\(z^5\)[/tex].
- Add the exponents for the common bases:
- For [tex]\(x\)[/tex]: [tex]\(x^2 \times x^3 = x^{2+3} = x^5\)[/tex]
- For [tex]\(z\)[/tex]: [tex]\(z \times z^5 = z^{1+5} = z^6\)[/tex]
Therefore, the numerator simplifies to:
[tex]\[
x^5 y z^6
\][/tex]
2. Combine the terms in the denominator:
- The terms in the denominator are [tex]\(x^5\)[/tex], [tex]\(y\)[/tex], and [tex]\(z^4\)[/tex].
So, the denominator remains:
[tex]\[
x^5 y z^4
\][/tex]
3. Rewrite the simplified expression:
[tex]\[
\frac{x^5 y z^6}{x^5 y z^4}
\][/tex]
4. Cancel the common terms in the numerator and denominator:
- [tex]\(x^5\)[/tex] in the numerator and [tex]\(x^5\)[/tex] in the denominator cancel out:
[tex]\[
\frac{x^5}{x^5} = 1
\][/tex]
- [tex]\(y\)[/tex] in the numerator and [tex]\(y\)[/tex] in the denominator cancel out:
[tex]\[
\frac{y}{y} = 1
\][/tex]
- For [tex]\(z\)[/tex], we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{z^6}{z^4} = z^{6-4} = z^2
\][/tex]
5. Write the final simplified result:
[tex]\[
z^2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
z^2
\][/tex]
This concludes the step-by-step simplification of the given expression.
