Simplify the Radical Expression ((a^2+3)^(1/3))/((a^2-3)^(-1/3))

$\frac{{(a^{2} + 3)}^{\frac{1}{3}}}{{(a^{2} - 3)}^{\frac{- 1}{3}}}$

Move ${(a^{2} - 3)}^{\frac{- 1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(a^{2} + 3)}^{\frac{1}{3}} {(a^{2} - 3)}^{- \frac{- 1}{3}}$

Move the negative in front of the fraction.

${(a^{2} + 3)}^{\frac{1}{3}} {(a^{2} - 3)}^{- - \frac{1}{3}}$

Multiply $- - \frac{1}{3}$ .

Multiply $- 1$ by $- 1$ .

${(a^{2} + 3)}^{\frac{1}{3}} {(a^{2} - 3)}^{1 (\frac{1}{3})}$

Multiply $\frac{1}{3}$ by $1$ .

${(a^{2} + 3)}^{\frac{1}{3}} {(a^{2} - 3)}^{\frac{1}{3}}$