2. \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \)

Let's simplify the expression step by step: \[ \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \] ### Step 1: Simplify the Denominator First, expand the denominator \(\left(x y^{2}\right)^{3}\) using the power of a product rule \((ab)^n = a^n b^n\): \[ \left(x y^{2}\right)^{3} = x^{3} \left(y^{2}\right)^{3} = x^{3} y^{6} \] So, the expression becomes: \[ \frac{35 x^{7} y^{8}}{7 x^{3} y^{6}} \] ### Step 2: Simplify the Coefficients Divide the numerical coefficients: \[ \frac{35}{7} = 5 \] ### Step 3: Simplify the Variables Apply the laws of exponents to simplify \(x\) and \(y\): \[ x^{7} \div x^{3} = x^{7-3} = x^{4} \] \[ y^{8} \div y^{6} = y^{8-6} = y^{2} \] ### Step 4: Combine the Simplified Parts Putting it all together: \[ 5 x^{4} y^{2} \] ### Final Simplified Expression \[ 5x^{4} y^{2} \]