A student simplified the rational expression using

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YEOng

29.01.2022

The resulting answer that the student got was wrong this was due to the wrong miscalculation when applying the division rule according to the law of indices. The difference between 6/5 and 2/5 is not 3 but 4/5

The expression simplified by the student is an indicinal expression

Indices are mathematical expressions that show the number of times a number or variable is being multiplied by itself.

According to the law of indices

$a^m \times a^n=a^{m+n}$ $\frac{a^m}{a^n}=a^{m-n$

where a, and n are integers or fractions

Given the expression simplified by the student expressed as:

$(\dfrac{x^\frac{2}{5} \times x^\frac{4}{5} }{x^{\frac{2}{5} }})^\frac{1}{2}$

Using the laws above:

$=(\dfrac{x^{\frac{2}{5}+\frac{4}{5} } }{x^{\frac{2}{5} }} )^\frac{1}{2} \\=(\dfrac{x^\frac{6}{5} }{x^\frac{2}{5} })^\frac{1}{2} \\$

Based on the law of division,

$=(x^{\frac{6}{5}-\frac{2}{5} })^\frac{1}{2} \\=(x^{\frac{6-2}{5} })^\frac{1}{2} \\=(x^\frac{4}{5})^\frac{1}{2} \\=x^{\frac{2}{5} }$

Hence the resulting answer that the student got was wrong this was due to the wrong miscalculation when applying the division rule according to the law of indices. The difference between 6/5 and 2/5 is not 3 but 4/5.

Learn more about indices here: link

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A student simplified the rational expression using the steps shown.

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