Question
Simplify \( \frac{24 w^{4} z^{9}}{15 w^{2} z^{3}} \)
Ask by Young Newton. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{8w^2z^6}{5}\)
Solution
1. Divide the numerical coefficients:
\[
\frac{24}{15} = \frac{8}{5}
\]
2. Simplify the \( w \) terms using the law of exponents:
\[
\frac{w^4}{w^2} = w^{4-2} = w^2
\]
3. Simplify the \( z \) terms using the law of exponents:
\[
\frac{z^9}{z^3} = z^{9-3} = z^6
\]
Combine the simplified parts:
\[
\frac{24 w^4 z^9}{15 w^2 z^3} = \frac{8}{5} \cdot w^2 \cdot z^6 = \frac{8w^2z^6}{5}
\]
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Simplify this solution Beyond the Answer
First, let's simplify the coefficients: \( \frac{24}{15} \) can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us \( \frac{8}{5} \). Next, we simplify the variable \( w \): \( \frac{w^{4}}{w^{2}} = w^{4-2} = w^{2} \). Now for the variable \( z \): \( \frac{z^{9}}{z^{3}} = z^{9-3} = z^{6} \). Putting it all together, the simplified result is: \[ \frac{8 w^{2} z^{6}}{5} \]
