Rewrite the expression using positive exponents: x^-3 (1)/(x^-3) -(1)/(x^3) -x^3 (1)/(x^3)

To rewrite the expressions using positive exponents, we can apply the rule that \( a^{-n} = \frac{1}{a^n} \) and vice versa.<br /><br />1. For \( x^{-3} \), using the rule, it becomes:<br /> \[<br /> x^{-3} = \frac{1}{x^3}<br /> \]<br /><br />2. For \( \frac{1}{x^{-3}} \), applying the rule gives:<br /> \[<br /> \frac{1}{x^{-3}} = x^3<br /> \]<br /><br />3. The expression \( -\frac{1}{x^{3}} \) already has positive exponents, so it remains:<br /> \[<br /> -\frac{1}{x^{3}}<br /> \]<br /><br />4. The expression \( -x^{3} \) also already has positive exponents, so it remains:<br /> \[<br /> -x^{3}<br /> \]<br /><br />5. Finally, \( \frac{1}{x^{3}} \) already uses positive exponents, so it remains:<br /> \[<br /> \frac{1}{x^{3}}<br /> \]<br /><br />Thus, the rewritten expressions with positive exponents are:<br />- \( x^{-3} = \frac{1}{x^3} \)<br />- \( \frac{1}{x^{-3}} = x^3 \)<br />- \( -\frac{1}{x^{3}} \) (already positive)<br />- \( -x^{3} \) (already positive)<br />- \( \frac{1}{x^{3}} \) (already positive)