Question
3. \( \frac{(3 x y z)^{4} x^{5} y^{2}}{9 x^{2} y^{2} z} \)
Ask by Salazar Bernard. in the Philippines
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \( 9x^{7}y^{4}z^{3} \).
Solution
Calculate or simplify the expression \( ((3*x*y*z)^4*x^5*y^2)/(9*x^2*y^2*z) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(\left(3xyz\right)^{4}x^{5}y^{2}\right)}{9x^{2}y^{2}z}\)
- step1: Remove the parentheses:
\(\frac{\left(3xyz\right)^{4}x^{5}y^{2}}{9x^{2}y^{2}z}\)
- step2: Reduce the fraction:
\(\frac{\left(3xyz\right)^{4}x^{3}}{9z}\)
- step3: Factor the expression:
\(\frac{9^{2}x^{4}y^{4}z^{4}x^{3}}{9z}\)
- step4: Reduce the fraction:
\(9x^{4}y^{4}z^{3}x^{3}\)
- step5: Multiply the terms:
\(9x^{4+3}y^{4}z^{3}\)
- step6: Add the numbers:
\(9x^{7}y^{4}z^{3}\)
The simplified form of the expression \( \frac{(3 x y z)^{4} x^{5} y^{2}}{9 x^{2} y^{2} z} \) is \( 9x^{7}y^{4}z^{3} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify \( \frac{(3 x y z)^{4} x^{5} y^{2}}{9 x^{2} y^{2} z} \), let's first break it down. The numerator can be expanded: \((3 x y z)^{4} = 3^{4} x^{4} y^{4} z^{4} = 81 x^{4} y^{4} z^{4}\). Now, rewriting the entire expression gives us: \(\frac{81 x^{4} y^{4} z^{4} x^{5} y^{2}}{9 x^{2} y^{2} z} = \frac{81 x^{9} y^{6} z^{4}}{9 x^{2} y^{2} z}\). Next, we can simplify by canceling out \(9\) from \(81\) and simplifying powers of \(x\), \(y\), and \(z\): \(\frac{81}{9} = 9\) and \(x^{9}/x^{2} = x^{7}\), \(y^{6}/y^{2} = y^{4}\), \(z^{4}/z = z^{3}\). Putting it all together, we have: \(9 x^{7} y^{4} z^{3}\). Thus, the simplified expression is \(9 x^{7} y^{4} z^{3}\).
