Questions: Simplify the monomial. Ensure your answer includes positive exponents only. [ frac9 a^2 b c^415 a b^3 c^5 ]

Solution Steps

Divide the coefficients \( \frac{9}{15} \) by their greatest common divisor, which is 3: \[ \frac{9}{15} = \frac{3}{5}. \]

For each variable, subtract the exponent in the denominator from the exponent in the numerator:

• For \( a \): \( a^{2} / a = a^{2-1} = a^{1} = a \).
• For \( b \): \( b / b^{3} = b^{1-3} = b^{-2} \).
• For \( c \): \( c^{4} / c^{5} = c^{4-5} = c^{-1} \).

Convert the negative exponents to positive exponents by moving them to the denominator: \[ b^{-2} = \frac{1}{b^{2}}, \quad c^{-1} = \frac{1}{c}. \]

Combine the simplified coefficients and variables: \[ \frac{3}{5} \cdot a \cdot \frac{1}{b^{2}} \cdot \frac{1}{c} = \frac{3a}{5b^{2}c}. \]

Final Answer