(64m^4)^3/2

Jasonbradley

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Jun 16, 2024

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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

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

Final Result

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