Simplify the expression as much as possible Write your answer in exponent form. For example, we would simplify (4c)^(3)/(2) to be 8c^(3)/(2) (8c^(3)/(4)z^(1)/(2))^(4)/(3)

To simplify the expression $(8c^{\frac {3}{4}}z^{\frac {1}{2}})^{\frac {4}{3}}$, we can apply the power of a power rule, which states that $(a^m)^n = a^{mn}$. <br /><br />First, let's simplify the coefficient 8:<br />$(8)^{\frac {4}{3}} = 8^{\frac {4}{3}} = (2^3)^{\frac {4}{3}} = 2^{3 \cdot \frac {4}{3}} = 2^4 = 16$<br /><br />Next, let's simplify the variable $c$:<br />$(c^{\frac {3}{4}})^{\frac {4}{3}} = c^{\frac {3}{4} \cdot \frac {4}{3}} = c^1 = c$<br /><br />Finally, let's simplify the variable $z$:<br />$(z^{\frac {1}{2}})^{\frac {4}{3}} = z^{\frac {1}{2} \cdot \frac {4}{3}} = z^{\frac {2}{3}}$<br /><br />Putting it all together, we have:<br />$(8c^{\frac {3}{4}}z^{\frac {1}{2}})^{\frac {4}{3}} = 16c^1z^{\frac {2}{3}} = 16c^{\frac {2}{3}}z^{\frac {2}{3}}$<br /><br />Therefore, the simplified expression is $16c^{\frac {2}{3}}z^{\frac {2}{3}}$.