How do you rewrite a expression using the base number only once? ex. 5^(-2)*5^(-4)*5^(8)
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The trick is to exploit the difference of squares formula,
Set a = √8 and b = √6, so that a + b is the expression in the denominator. Multiply by its conjugate a - b:
Whatever you do to the denominator, you have to do to the numerator too. So
Expand the numerator:
So we have
But √12 = √(3•4) = 2√3, so