Simplify the Radical Expression (y^(4/3)*y^(2/3))^(-1/2)

${(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}})}^{- \frac{1}{2}}$

Multiply $y^{\frac{4}{3}}$ by $y^{\frac{2}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(y^{\frac{4}{3} + \frac{2}{3}})}^{- \frac{1}{2}}$

Combine the numerators over the common denominator.

${(y^{\frac{4 + 2}{3}})}^{- \frac{1}{2}}$

Add $4$ and $2$ .

${(y^{\frac{6}{3}})}^{- \frac{1}{2}}$

Divide $6$ by $3$ .

${(y^{2})}^{- \frac{1}{2}}$

Multiply the exponents in ${(y^{2})}^{- \frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{2 (- \frac{1}{2})}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y^{2 (\frac{- 1}{2})}$

Cancel the common factor.

$y^{2 (\frac{- 1}{2})}$

Rewrite the expression.

$y^{- 1}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{y}$