Question
Simplify. \[ \frac{z^{6} y^{3}}{z^{6} y^{4}} \]
Ask by Spencer Rodriquez. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{1}{y} \).
Solution
We can simplify the expression by canceling common factors in the numerator and the denominator. The expression is
(z⁶·y³) / (z⁶·y⁴).
First, notice that z⁶ appears in both the numerator and the denominator, so we can cancel it. This leaves us with:
y³ / y⁴.
Now, using the laws of exponents (subtract the exponents when dividing like bases), we have:
y³ / y⁴ = y^(3 − 4) = y^(−1).
Since y^(−1) is equivalent to 1/y, the simplified expression is:
1/y.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression \( \frac{z^{6} y^{3}}{z^{6} y^{4}} \), we can divide the numerator and the denominator by \( z^{6} \) since they are the same in both places: \[ \frac{z^{6} y^{3}}{z^{6} y^{4}} = \frac{y^{3}}{y^{4}}. \] Next, we can simplify \( \frac{y^{3}}{y^{4}} \) using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \): \[ \frac{y^{3}}{y^{4}} = y^{3-4} = y^{-1}. \] Thus, the simplified expression is: \[ y^{-1} = \frac{1}{y}. \] So the final answer is: \[ \frac{1}{y}. \]
