Questions: Watch the video and then solve the problem given below. Click here to watch the video Simplify the exponential expression. -25 x^(11) y^(7) / 5 x^(2) y^(5) = □ (Simplify your answer. Use positive exponents only.)

Solution Steps

To simplify the given exponential expression, we need to divide the coefficients and subtract the exponents of like bases according to the laws of exponents. Specifically, for the expression \(\frac{-25 x^{11} y^{7}}{5 x^{2} y^{5}}\), we will divide \(-25\) by \(5\), subtract the exponents of \(x\) (i.e., \(11 - 2\)), and subtract the exponents of \(y\) (i.e., \(7 - 5\)).

To simplify the expression \(\frac{-25 x^{11} y^{7}}{5 x^{2} y^{5}}\), we first divide the coefficients. The coefficient in the numerator is \(-25\) and in the denominator is \(5\). Dividing these gives: \[ \frac{-25}{5} = -5 \]

Next, we simplify the exponents of \(x\). The exponent of \(x\) in the numerator is \(11\) and in the denominator is \(2\). Subtracting these exponents gives: \[ 11 - 2 = 9 \]

Similarly, we simplify the exponents of \(y\). The exponent of \(y\) in the numerator is \(7\) and in the denominator is \(5\). Subtracting these exponents gives: \[ 7 - 5 = 2 \]

Final Answer