Simplify. (54x)/(9x^3) square

To simplify the expression \(\frac{54x}{9x^3}\), follow these steps:<br /><br />1. **Simplify the coefficients:**<br /> - The coefficient in the numerator is 54, and in the denominator, it is 9.<br /> - Divide 54 by 9: <br /> \[<br /> \frac{54}{9} = 6<br /> \]<br /><br />2. **Simplify the variables:**<br /> - In the numerator, we have \(x\).<br /> - In the denominator, we have \(x^3\).<br /> - Apply the rule of exponents for division: \(\frac{x^a}{x^b} = x^{a-b}\).<br /> - Here, \(a = 1\) and \(b = 3\), so:<br /> \[<br /> x^{1-3} = x^{-2}<br /> \]<br /><br />3. **Combine the simplified parts:**<br /> - Combine the simplified coefficient and variable:<br /> \[<br /> 6x^{-2}<br /> \]<br /><br />4. **Express with positive exponents:**<br /> - Rewrite \(x^{-2}\) as \(\frac{1}{x^2}\):<br /> \[<br /> 6x^{-2} = \frac{6}{x^2}<br /> \]<br /><br />Thus, the simplified form of \(\frac{54x}{9x^3}\) is \(\frac{6}{x^2}\).