GRE Algebra - Higher order equations cont.

Here we solve a quadratic equation that requires additional steps to first change the equation into a familiar format. Note that in solving this equation you need to be familiar with manipulating equations (adding and subtracting the same number to both sides of the equal sign), and you need to be able to spot the difference in squares quantity. Again, this is an example of how the GRE tests simple concepts, but you have to use these concepts in a coordinated way to demonstrate your proficiency.

Step 0 Original Equation, solve for n n2.3 / n0.3 = 16
Step 1 Combine all like terms, so in this case combine the ns. This is where we use the rules of exponentiation n2.3-0.3 = 16
Step 1.5   n2 = 16
Step 2 Subtract 16 from both sides n2 - 16 = 0
Step 3 We perform the required factorization, noticing that the quantity to the left of the equal sign in step 2 is actually a difference in squares (n - 4)(n + 4) = 0
Step 4 Solve for possible value of n n = 4
n = -4