(8x^6y^-15z^3)^(2/3) *(49x^-2y^8x^2)^(-1/2)
You asked:
Evaluate the expression: \({\left( 8 \cdot {x}^{6} \cdot {y}^{-15} \cdot {z}^{3} \right)}^{\frac{2}{3}} \cdot {\left( 49 \cdot {x}^{-2} \cdot {y}^{8} \cdot {x}^{2} \right)}^{\frac{-1}{2}}\)
MathBot Answer:
\[{\left( 8 \cdot {x}^{6} \cdot {y}^{-15} \cdot {z}^{3} \right)}^{\frac{2}{3}} \cdot {\left( 49 \cdot {x}^{-2} \cdot {y}^{8} \cdot {x}^{2} \right)}^{\frac{-1}{2}} = \frac{4 \left(\frac{x^{6} z^{3}}{y^{15}}\right)^{\frac{2}{3}}}{7 \sqrt{y^{8}}}\]
If the variables \(x\), \(y\), \(z\) are real, then: \[\frac{4 \left(\frac{x^{6} z^{3}}{y^{15}}\right)^{\frac{2}{3}}}{7 \sqrt{y^{8}}} = \frac{4 \left(\frac{x^{6} z^{3}}{y^{15}}\right)^{\frac{2}{3}}}{7 \left|{y^{4}}\right|}\]