SAT Mathematics Practice Test 2

Since the numerator and denominator of

xa2

xb2

have a common base, it follows by the laws of exponents that this expression can be rewritten as xa2−b2.Thus,the equation

xa2

xb2

=16 can be written asxa2−b2=x16 Because the equivalent expressions have the common base x, and x>1 it follows that the exponents of the two expressions must also be equivalent.Hence, the equation a2−b2=16 must be true. The left-hand side of this new equation is a difference of squares, and so it can be factored: (a+b)(a−b)=16.Finally,dividing both sides of 2(a−b)=16 by 2 gives a−b=8
Choices B, C, and D are incorrect and may result from errors in applying the laws of exponents or errors in solving the equation a2−b2=16.