(64/b^27)^2/3

Jasonbradley

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Jun 16, 2024

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Simplifying (64/b^27)^2/3

This expression involves fractional exponents and requires understanding of exponent rules to simplify it. Here's a step-by-step breakdown:

Understanding the Properties

• Fractional Exponent: A fractional exponent like 2/3 represents both a root and a power. The denominator (3) indicates the root (cube root in this case) and the numerator (2) indicates the power.
• Power of a Quotient: (a/b)^n = a^n / b^n
• Power of a Power: (a^m)^n = a^(m*n)

Simplifying the Expression

1. Apply the power of a quotient rule: (64/b^27)^2/3 = 64^(2/3) / b^(27 * 2/3)

2. Simplify the powers:

   • 64^(2/3) = (4^3)^(2/3) = 4^(3 * 2/3) = 4^2 = 16
   • b^(27 * 2/3) = b^18

3. Combine the results: 64^(2/3) / b^(27 * 2/3) = 16 / b^18

Therefore, the simplified form of (64/b^27)^2/3 is 16/b^18.