Question

If $15625=(x{)}^2=5^{\left(y\right)}$ . Find the value of $x$ and $y$. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Mark

$15625=(x{)}^2=5^{\left(y\right)}$
Prime factorisation of
$15625=5\times 5\times 5\times 5\times 5\times 5=5^6={\left(5^3\right)}^2$
$={125}^2$
$\Rightarrow x=125$
$\Rightarrow y=6$