Patrick has to work out the exact value of $64^{rac{1}{4}}$ - Edexcel - GCSE Maths - Question 13 - 2019 - Paper 3

Patrick incorrectly interprets $64^{\frac{1}{4}}$ as simply taking one fourth of the value 64. In mathematical terms, $64^{\frac{1}{4}}$ means finding the fourth root of 64, not one fourth of it.

To clarify, the expression is:

$64^{\frac{1}{4}} = \sqrt[4]{64}$

We know that $64 = 4^3$, so:

$\sqrt[4]{64} = \sqrt[4]{(4^3)} = 4^{\frac{3}{4}}$

This results in:

$4^{\frac{3}{4}} \text{(which is not equal to 16)}$

In conclusion, Patrick's method is incorrect; he should find the fourth root of 64 instead of simply dividing by four.