SAT Math Question of the Day

Q: x^{(a + b)} / x^a

1. x^a
2. x^b
3. x^{(1 + b)}
4. x^{(1 + b/a)}
5. x^{(2a + b)}

UNANSWERED.

The correct answer is B.

A: x^b is the correct answer.

Remember these rules:

1. If the base (x) is the same and you're multiplying, you add the exponents.
   x^a x^b= x^a+b
2. If the base (x) is the same and you're dividing, you subtract the exponents.
   x^{a + b} / x^a = x^{a + b - a} = x^b

If you forget what to do on the SAT, try Pick and Play. Pick some small numbers (but not 0 or 1) for all the variables and then plug them in.
For example, x = 2, a = 3, b = 2
x^{(a + b)} / x^a = 2^{(3 + 2)} / 2³ = 2⁵ / 2³ = 32 / 8 = 4
Now plug in the same variables into the possible answers. Use your calculator when needed.

1. x^a = 2³ = 8 Does NOT match 4, so this is wrong.
2. x^b = 2² = 4. Matches, so it might be right, but we have to check the other answers too.
3. x^{(1 + b)} = 2^{(1 + 2)} = 2³ = 8. No match.
4. x^{(1 + b/a)} = 2^{(1 + 2/3)} = 2^(5/3). Ugh... this looks too complex.
5. x^{(2a + b)} = 2^{(2* 3 + 2)} = 2⁸ = 256. Way too high.