find value of 2*((((2^4)^3)^1/4)^1/5)
You asked:
Evaluate the expression: \(2 \cdot \frac{{\left( \frac{{{{2}^{4}}^{3}}^{1}}{4} \right)}^{1}}{5}\)
MathBot Answer:
\[2 \cdot \frac{{\left( \frac{{{{2}^{4}}^{3}}^{1}}{4} \right)}^{1}}{5} = \frac{2048}{5} = 409.6\]
\[\begin{aligned}2 \cdot \frac{{\left( \frac{{{{2}^{4}}^{3}}^{1}}{4} \right)}^{1}}{5}& = 2 \cdot \left(\left(\left(2^{4}\right)^{3}\right)^{1} \cdot \frac{1}{4}\right)^{1} \cdot \frac{1}{5}\\& = 2 \cdot \left(\left(16^{3}\right)^{1} \cdot \frac{1}{4}\right)^{1} \cdot \frac{1}{5}\\& = 2 \cdot \left(4096^{1} \cdot \frac{1}{4}\right)^{1} \cdot \frac{1}{5}\\& = 2 \cdot \left(\frac{4096}{4}\right)^{1} \cdot \frac{1}{5}\\& = 2 \cdot 1024^{1} \cdot \frac{1}{5}\\& = 2 \cdot \frac{1024}{5}\\& = \frac{2048}{5}\end{aligned}\]