Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(a^3b^2/ab)^3
To simplify the expression (a^3b^2/ab)^3, we can simplify the part inside the parentheses first.
The numerator of the fraction, a^3b^2, can be simplified by combining the exponents of a: a^3 ÷ a^1 = a^(3-1) = a^2.
The denominator of the fraction, ab, remains the same.
Now, we simplify the expression inside the parentheses: (a^2/ab)^3.
To multiply fractions with the same denominator, we multiply the numerators and denominators separately.
The numerator of the fraction becomes a^2 * a^2 * a^2 = (a^2)^3 = a^(2*3) = a^6.
The denominator of the fraction remains as ab.
Therefore, (a^2/ab)^3 simplifies to a^6/(ab)^3.
Note: The exponents within parentheses are distributed to each term inside the parentheses, so we do not expand the exponent of (ab)^3 any further.