Question

which expression is equivalent to \\(\frac{60x^{20}y^{24}}{30x^{10}y^{12}}\\)? \\(\circ\\ 2x^2y^2\\) \\(\circ\\ 2x^{10}y^{12}\\) \\(\circ\\ 30x^2y^2\\) \\(\circ\\ 30x^{10}y^{12}\\)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient 60 by 30.
$\frac{60}{30} = 2$

Step2: Simplify the \(x\)-term

Use the quotient rule for exponents \( \frac{a^m}{a^n}=a^{m - n} \). For \(x\), we have \( \frac{x^{20}}{x^{10}} = x^{20 - 10}=x^{10}\)

Step3: Simplify the \(y\)-term

Using the quotient rule for exponents again, \( \frac{y^{24}}{y^{12}} = y^{24 - 12}=y^{12}\)

Step4: Combine the results

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together: \(2\times x^{10}\times y^{12}=2x^{10}y^{12}\)

Answer:

B. \(2x^{10}y^{12}\)