Work out the value of $$\left( \frac{5^{\frac{4}{9}}}{2^{-1}} \times \left( \frac{4}{3} \right)^{\frac{2}{3}} \right)$$ You must show all your working. - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 1

Next, we simplify \\left( \frac{4}{3} \right)^{\frac{2}{3}}:

$\left( \frac{4}{3} \right)^{\frac{2}{3}} = \frac{4^{\frac{2}{3}}}{3^{\frac{2}{3}}}$

Calculating $4^{\frac{2}{3}}$ gives:

$4^{\frac{2}{3}} = (2^2)^{\frac{2}{3}} = 2^{\frac{4}{3}}$

Now substituting back we have:

$\left( 5^{\frac{4}{9}} \cdot 2 \right) \cdot \frac{2^{\frac{4}{3}}}{3^{\frac{2}{3}}}$

This simplifies further to:

$\frac{5^{\frac{4}{9}} \cdot 2^{1 + \frac{4}{3}}}{3^{\frac{2}{3}}} = \frac{5^{\frac{4}{9}} \cdot 2^{\frac{7}{3}}}{3^{\frac{2}{3}}}$

Having completed the simplification, we assess if we can express this in a simpler form or compute an approximate numerical answer. However, in its current form, the answer remains:

$\frac{5^{\frac{4}{9}} \cdot 2^{\frac{7}{3}}}{3^{\frac{2}{3}}}$

Thus, this expression represents the final value.