## Simplifying (64m^4)^3/2

This expression involves exponents and fractional exponents. Let's break down the steps to simplify it:

### Understanding the Properties of Exponents

**Power of a Power:**When raising a power to another power, we multiply the exponents: (a^m)^n = a^(m*n)**Fractional Exponent:**A fractional exponent like 1/n represents the nth root: a^(1/n) = √n(a)

### Applying the Properties

**Simplify the exponent:**(64m^4)^3/2 = 64^(3/2) * (m^4)^(3/2)**Apply Power of a Power:**64^(3/2) * (m^4)^(3/2) = 64^(3/2) * m^(4*3/2)**Simplify the exponents:**64^(3/2) * m^(4*3/2) = 64^(3/2) * m^6**Calculate the fractional exponent:**64^(3/2) = (√64)^3 = 8^3 = 512

### Final Result

Therefore, (64m^4)^3/2 simplifies to **512m^6**.