root(2 ^ 14, 16) = root(2 ^ 7, 8)
You asked:
Investigate the equation: \(\sqrt[16]{{2}^{14}} = \sqrt[8]{{2}^{7}}\).
MathBot Answer:
This equation has no unknown quantities, so it is either true or false.
This equation is true because the left-hand side is equal to the right-hand side.
The left-hand side of the equation is:
\[\sqrt[16]{{2}^{14}} = 2^{\frac{7}{8}}\]The right-hand side of the equation is:
\[\sqrt[8]{{2}^{7}} = 2^{\frac{7}{8}}\]