Simplifying Powers / Indices / Exponents - Example 2

In this video, I show you how to turn a long, ugly series of multiplications into a simple elegant expression using powers and index laws.

We start with the expression:

64\times \sqrt[3]{125}\times \frac{1}{16}\times 5^{-2}

We will use the following index laws:

\begin{matrix} 1. &a^{-n} &= &\frac{1}{a^{n}} \\ 2. &a^{\frac{n}{m}} &= &\sqrt[m]{a^{n}} \\ 3. &a^{n}\times a^{m} &= & a^{n+m} \end{matrix}

Our goal is to try and turn this into an expression of 2ⁿ x 5^m (a power of 2 multiplied by a power of 5)