Question

Evaluate the following expression. $\[\left( \frac{16}{9} \right)^{(2/3)} \cdot \left( \frac{4}{3} \right)^{(5/3)}\]$

Answer 1

7.8 * 10^7

Explanation:

(7.8 * 10^3) * (1.0 * 10^4) = (7.8 * 1.0) * (10^3 * 10^4)

7.8 * 10^3 +4

7.8 * 10^7

Answer 2

`\left(\frac{16}9\right)^(2/3) \cdot \left(\frac43\right)^(5/3) = \left(\left(\frac{16}9\right)^2\right)^(1/3) \cdot \left(\left(\frac43\right)^5\right)^(1/3) \\\\ \cdots = \left(\left(\frac{16}9\right)^2 \cdot \left(\frac43\right)^5\right)^(1/3) \\\\ \cdots = \left(\left((4^2)/(3^2)\right)^2 \cdot \left(\frac43\right)^5\right)^(1/3) \\\\ \cdots = \left(\left(\left(\frac43\right)^2\right)^2 \cdot \left(\frac43\right)^5\right)^(1/3) \\\\ \cdots = \left(\left(\frac43\right)^4 \cdot \left(\frac43\right)^5\right)^(1/3) \\\\ \cdots = \left(\left(\frac43\right)^9\right)^(1/3) \\\\ \cdots = \left(\frac43\right)^(9/3) \\\\ \cdots = \left(\frac43\right)^3 \\\\ \cdots = (4^3)/(3^3) \\\\ \cdots = \boxed{(64)/(27)}`