Introduction tc ((3)/(4))^-2=(-1)/(3)

It looks like there might be a misunderstanding in the equation you provided. Let's clarify and solve the expression step by step.<br /><br />The expression given is:<br />\[<br />\left(\frac{3}{4}\right)^{-2}<br />\]<br /><br />To solve this, we need to understand what raising a fraction to a negative exponent means. A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. In other words:<br />\[<br />a^{-n} = \frac{1}{a^n}<br />\]<br /><br />Applying this rule to our expression:<br />\[<br />\left(\frac{3}{4}\right)^{-2} = \frac{1}{\left(\frac{3}{4}\right)^2}<br />\]<br /><br />Next, we need to calculate \(\left(\frac{3}{4}\right)^2\):<br />\[<br />\left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16}<br />\]<br /><br />Now, take the reciprocal of \(\frac{9}{16}\):<br />\[<br />\frac{1}{\frac{9}{16}} = \frac{16}{9}<br />\]<br /><br />Therefore, the value of \(\left(\frac{3}{4}\right)^{-2}\) is:<br />\[<br />\frac{16}{9}<br />\]<br /><br />This shows that the original equation \(\left(\frac{3}{4}\right)^{-2} = \frac{-1}{3}\) is incorrect. The correct value is \(\frac{16}{9}\).