Question

If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{-2}{5}\right)}^{28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2.$
[4 marks]

Answer 1

Using $a^m\times a^n=a^{m+n}$ and $a^m÷a^n=a^{m-n}$

$x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{-2}{5}\right)}^{28}=(-\frac{2}{5}{)}^2$
[1 mark]

$y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3=(-\frac{2}{5}{)}^5$
[1 mark]

$x^3=\left(\right(-\frac{2}{5}{)}^2{)}^3=(-\frac{2}{5}{)}^6$
[1 mark]

$x^3÷y=(-\frac{2}{5}{)}^6÷(-\frac{2}{5}{)}^5=\frac{-2}{5}$
[0.5 mark]

$(x^3÷y{)}^2={\left(\frac{-2}{5}\right)}^2=\frac{4}{25}$
[0.5 mark]