Exponents

Problem:



Solution:

The general method of solving these problems is

Step 1) Write the root as a fraction power.

For example, $\sqrt[3]{5^6} = (5^6)^{\frac{1}{3}}$
$\sqrt{3^6} = (3^6)^{\frac{1}{2}}$

Step 2) Multiply the exponents

For example, $(5^6)^{\frac{1}{3}} = 5^{6 \times \frac{1}{3}} = 5^2$
$(3^6)^{\frac{1}{2}} = 3^{6 \times \frac{1}{2}}= 3^3$.

That's it.