Simplify the expression. \[ \left(z^{-\frac{5}{3}} \cdot x^{2}\right)^{\frac{1}{2}} \] Write your answer without using negative exponents. Assume that all variables are positive real numbers.
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Mind Expander
To simplify the expression \(\left(z^{-\frac{5}{3}} \cdot x^{2}\right)^{\frac{1}{2}}\), we can start by applying the exponent to each component inside the parentheses: \[ = \left(z^{-\frac{5}{3}}\right)^{\frac{1}{2}} \cdot \left(x^{2}\right)^{\frac{1}{2}} \] Now, we simplify each part individually: 1. For \(\left(z^{-\frac{5}{3}}\right)^{\frac{1}{2}}\): \[ = z^{-\frac{5}{3} \cdot \frac{1}{2}} = z^{-\frac{5}{6}} \] 2. For \(\left(x^{2}\right)^{\frac{1}{2}}\): \[ = x^{2 \cdot \frac{1}{2}} = x^{1} = x \] Now we combine these results: \[ = z^{-\frac{5}{6}} \cdot x \] Since we want to express our answer without negative exponents, we rewrite \(z^{-\frac{5}{6}}\) as \(\frac{1}{z^{\frac{5}{6}}}\): \[ = \frac{x}{z^{\frac{5}{6}}} \] Thus, the simplified expression is: \[ \frac{x}{z^{\frac{5}{6}}} \]
