Exercise
$\sqrt{\sqrt{\sqrt{\sqrt{m^3}n}}}$
Step-by-step Solution
Learn how to solve powers of powers problems step by step online. Simplify the power of a power (m^3^(1/2)n)^(1/2)^(1/2)^(1/2). Simplify \sqrt{\sqrt{\sqrt{\sqrt{m^3}n}}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \frac{1}{2}. Simplify \left(\sqrt{\sqrt{m^3}n}\right)^{\left(\left(\frac{1}{2}\right)^2\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \left(\frac{1}{2}\right)^2. Simplify \sqrt{m^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{2}. Calculate the power \left(\frac{1}{2}\right)^2.
Simplify the power of a power (m^3^(1/2)n)^(1/2)^(1/2)^(1/2)
Final answer to the exercise
$\sqrt[16]{m^{3}}\sqrt[8]{n}$