Match the radicals with the equivalent rational exponent Hint: Some cards might have multiple matches. sqrt (8) z^(5)/(3) (3x)^(3)/(2) (3x)^(2)/(3) sqrt (5z) (3^3)^(1)/(2) sqrt ((3x)^3) sqrt [3]((3x)^2) sqrt [3](z^5) (2^3)^(1)/(2) 3^(5)/(2) 2^(3)/(2) sqrt (27) (5z)^(1)/(2) 8^(1)/(2)

Let's match the radicals with their equivalent rational exponents:<br /><br />1. $\sqrt{8}$<br /> - $8^{\frac{1}{2}}$<br /> - $2^{\frac{3}{2}}$<br /><br />2. $z^{\frac{5}{3}}$<br /> - $\sqrt[3]{z^5}$<br /><br />3. $(3x)^{\frac{3}{2}}$<br /> - $\sqrt{(3x)^3}$<br /><br />4. $(3x)^{\frac{2}{3}}$<br /> - $\sqrt[3]{(3x)^2}$<br /><br />5. $\sqrt{5z}$<br /> - $(5z)^{\frac{1}{2}}$<br /><br />6. $(3^3)^{\frac{1}{2}}$<br /> - $\sqrt{27}$<br /><br />7. $\sqrt{(3x)^3}$<br /> - $(3x)^{\frac{3}{2}}$<br /><br />8. $\sqrt[3]{(3x)^2}$<br /> - $(3x)^{\frac{2}{3}}$<br /><br />9. $\sqrt[3]{z^5}$<br /> - $z^{\frac{5}{3}}$<br /><br />10. $(2^3)^{\frac{1}{2}}$<br /> - $2^{\frac{3}{2}}$<br /><br />11. $2^{\frac{3}{2}}$<br /> - $8^{\frac{1}{2}}$<br /><br />12. $8^{\frac{1}{2}}$<br /> - $2^{\frac{3}{2}}$<br /><br />So, the matches are:<br /><br />- $\sqrt{8}$ matches with $8^{\frac{1}{2}}$ and $2^{\frac{3}{2}}$<br />- $z^{\frac{5}{3}}$ matches with $\sqrt[3]{z^5}$<br />- $(3x)^{\frac{3}{2}}$ matches with $\sqrt{(3x)^3}$<br />- $(3x)^{\frac{2}{3}}$ matches with $\sqrt[3]{(3x)^2}$<br />- $\sqrt{5z}$ matches with $(5z)^{\frac{1}{2}}$<br />- $(3^3)^{\frac{1}{2}}$ matches with $\sqrt{27}$<br />- $\sqrt{(3x)^3}$ matches with $(3x)^{\frac{3}{2}}$<br />- $\sqrt[3]{(3x)^2}$ matches with $(3x)^{\frac{2}{3}}$<br />- $\sqrt[3]{z^5}$ matches with $z^{\frac{5}{3}}$<br />- $(2^3)^{\frac{1}{2}}$ matches with $2^{\frac{3}{2}}$<br />- $2^{\frac{3}{2}}$ matches with $8^{\frac{1}{2}}$<br />- $8^{\frac{1}{2}}$ matches with $2^{\frac{3}{2}}$