Questions: Select the correct answer. Which expression is equivalent to 76 a^2 b^3 / 19 a b ? Assume that the options are: A. 4 a b^2 B. 4 b^2 / a C. a b^2 / 4 D. 4 a b

Solution Steps

To simplify the given expression \(\frac{76 a^{2} b^{3}}{19 a b}\), we need to divide the coefficients and subtract the exponents of the variables in the numerator and the denominator.

To simplify the coefficients, we divide the numerator coefficient by the denominator coefficient: \[ \frac{76}{19} = 4 \]

To simplify the exponents of \(a\), we subtract the exponent in the denominator from the exponent in the numerator: \[ a^{2-1} = a^1 = a \]

To simplify the exponents of \(b\), we subtract the exponent in the denominator from the exponent in the numerator: \[ b^{3-1} = b^2 \]

Combining the simplified coefficient and the simplified exponents, we get: \[ 4 a b^2 \]

Final Answer