Question
(9) \( \frac{\left(3 x^{-1} y^{-2} z^{2}\right)^{-3}}{\left(5 x^{2} y\right)^{2}} \)
Ask by Allan Chang. in Colombia
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La expresión simplificada es \( \frac{y^{4}}{675z^{6}x} \).
Solution
Calculate or simplify the expression \( (3*x^(-1)*y^(-2)*z^2)^(-3)/(5*x^2*y)^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(3x^{-1}y^{-2}z^{2}\right)^{-3}}{\left(5x^{2}y\right)^{2}}\)
- step1: Express with a positive exponent:
\(\frac{\frac{1}{\left(3x^{-1}y^{-2}z^{2}\right)^{3}}}{\left(5x^{2}y\right)^{2}}\)
- step2: Multiply by the reciprocal:
\(\frac{1}{\left(3x^{-1}y^{-2}z^{2}\right)^{3}}\times \frac{1}{\left(5x^{2}y\right)^{2}}\)
- step3: Multiply the terms:
\(\frac{1}{\left(3x^{-1}y^{-2}z^{2}\right)^{3}\left(5x^{2}y\right)^{2}}\)
- step4: Multiply the terms:
\(\frac{1}{\frac{675z^{6}x}{y^{4}}}\)
- step5: Simplify:
\(\frac{y^{4}}{675z^{6}x}\)
La expresión dada se simplifica a \( \frac{y^{4}}{675z^{6}x} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To simplify the expression, start with the numerator: \[ \left(3 x^{-1} y^{-2} z^{2}\right)^{-3} = \frac{1}{(3 x^{-1} y^{-2} z^{2})^{3}} = \frac{1}{27 x^{-3} y^{-6} z^{6}} = \frac{z^{6} y^{6}}{27 x^{3}} \] Next, simplify the denominator: \[ \left(5 x^{2} y\right)^{2} = 25 x^{4} y^{2} \] Now, combine the numerator and denominator: \[ \frac{\frac{z^{6} y^{6}}{27 x^{3}}}{25 x^{4} y^{2}} = \frac{z^{6} y^{6}}{27 \cdot 25 x^{3} x^{4} y^{2}} = \frac{z^{6} y^{4}}{675 x^{7}} \] So, the simplified expression is: \[ \frac{z^{6} y^{4}}{675 x^{7}} \]
