Simplifying (64/b^27)^2/3
This expression involves fractional exponents and requires understanding of exponent rules to simplify it. Here's a stepbystep 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

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

Simplify the powers:
 64^(2/3) = (4^3)^(2/3) = 4^(3 * 2/3) = 4^2 = 16
 b^(27 * 2/3) = b^18

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.