(A21-2 Rational Exponents and Properties of Ex Exponents Write the radical using rational exponents sqrt [4](x^-2) sqrt [4](x^-3)=square (Use integers or fractions for any numbers in the expression.)

## Step 1<br />The problem asks us to convert the given radical expressions into expressions with rational exponents. The general rule for converting a radical expression to an expression with a rational exponent is:<br />### \(\sqrt[n]{x^m} = x^{\frac{m}{n}}\)<br />where \(n\) is the root of the radical and \(m\) is the exponent of the radicand.<br /><br />## Step 2<br />For the first expression, \(\sqrt[4]{x^{-2}}\), we apply the rule. Here, \(n = 4\) (the fourth root) and \(m = -2\) (the exponent of the radicand). So, we get:<br />### \(x^{\frac{-2}{4}}\)<br /><br />## Step 3<br />For the second expression, \(\sqrt[4]{x^{-3}}\), we again apply the rule. Here, \(n = 4\) (the fourth root) and \(m = -3\) (the exponent of the radicand). So, we get:<br />### \(x^{\frac{-3}{4}}\)