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

Now we simplify the numerator:

$a = (4/3)^{\frac{2}{3}} = \frac{4^{\frac{2}{3}}}{3^{\frac{2}{3}}} = \frac{\sqrt[3]{16}}{\sqrt[3]{9}}$

Thus, substituting back:

$= 5^{\frac{4}{9}} \times \frac{\sqrt[3]{16}}{\sqrt[3]{9}} \times 2$

Now let's perform the final calculation:

By combining these we have:

$\text{Value} = 2 \times 5^{\frac{4}{9}} \times \frac{\sqrt[3]{16}}{\sqrt[3]{9}}$

This expression simplifies further, and you can compute the numerical value using a calculator to get the final result.