$x$ is an integer greater than 1.
Write the following in order of size, starting with the largest. $x^0$ , $x^{\tfrac{3}{2}}$ , $x^{\tfrac{3}{4}}$ , $x^2$ Answer ...

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Worked solution

1. Compare the powers by comparing their indices

Since $x$ is an integer greater than 1, $x>1$ . For powers of the same base greater than 1, the larger the index, the larger the value.

Compare the indices:
$2>\frac{3}{2}>\frac{3}{4}>0$
So the values in decreasing order are
$x^2>x^{\frac{3}{2}}>x^{\frac{3}{4}}>x^0.$

Answer

$x^2$ , $x^{\tfrac{3}{2}}$ , $x^{\tfrac{3}{4}}$ , $x^0$

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