As shown in the above picture, the laws of indices only applies to multiplication or division, when you see addition or subtraction, chances are, you have to factorise, one example is the question Mr Ingham set for us, shown in the picture below
As you can see Mr Ingham 'solved' his own question by using this law a^(m+n) = a^m + a^n
From there, he was able to get a quadratic equation, thereby using the calculator to solve that problem.
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