Question

which expression is equivalent to \\(\frac{10x^6y^{12}}{-5x^{-2}y^{-6}}\\)? assume \\(x \
eq 0, y \
eq 0\\).\
\\(\bigcirc\\) \\(-50x^8y^{18}\\)\
\\(\bigcirc\\) \\(-2x^8y^{18}\\)\
\\(\bigcirc\\) \\(-2x^{12}y^{72}\\)\
\\(\bigcirc\\) \\(5x^8y^{18}\\)

Explanation:

Step1: Simplify the coefficient

Divide the coefficient \(10\) by \(-5\): \(\frac{10}{-5} = -2\)

Step2: Simplify the \(x\)-terms

Use the rule of exponents \( \frac{a^m}{a^n} = a^{m - n} \). For \(x\)-terms: \(x^{6} \div x^{-2} = x^{6 - (-2)} = x^{8}\)

Step3: Simplify the \(y\)-terms

For \(y\)-terms: \(y^{12} \div y^{-6} = y^{12 - (-6)} = y^{18}\)

Step4: Combine the results

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together: \(-2 \times x^{8} \times y^{18} = -2x^{8}y^{18}\)

Answer:

\(-2x^{8}y^{18}\) (corresponding to the option: \(-2x^{8}y^{18}\))