Simplifying Expressions: (ab^2)^3 / b^5
This article will guide you through simplifying the expression (ab^2)^3 / b^5.
Understanding the Rules
To simplify this expression, we need to apply some basic rules of exponents:
 Power of a product: (ab)^n = a^n * b^n
 Power of a power: (a^m)^n = a^(m*n)
 Division of powers with the same base: a^m / a^n = a^(mn)
StepbyStep Simplification

Apply the power of a product rule to the numerator: (ab^2)^3 = a^3 * (b^2)^3

Apply the power of a power rule to the numerator: a^3 * (b^2)^3 = a^3 * b^(2*3) = a^3 * b^6

Rewrite the expression with the simplified numerator: (a^3 * b^6) / b^5

Apply the division of powers with the same base rule: a^3 * b^(65) = a^3 * b^1

Simplify: a^3 * b
Conclusion
Therefore, the simplified form of the expression (ab^2)^3 / b^5 is a^3 * b.