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Math Basics: Exponents

One thing is certain on test day – you will see exponents. Another thing is also certain – those exponent problems will be meant to trick you. So, know your exponent properties, but also be aware that knowing the fundamentals alone won’t guarantee success. Tread carefully, and check your work. You should be able to answer most of these exponent questions correctly. Speaking of which, let’s see if you can answer the following three questions. They are not very difficult, only a little tricky.

1. 4^3+4^3+4^3+4^3=

  1. 2^6
  2. 2^10
  3. 4^4
  4. 4^12
  5. 64^3

2. (2^5)^4+(2^3)^2=

  1. 2^15
  2. 2^20
  3. 2^26
  4. 2^6*(2^14+1)
  5. 2^120*(2^2+1)

3. If 3^{-x}+3^{-x}+3^{-x}=1, what is the value of x?

  1. -1
  2. -1/2
  3. 1/3
  4. 1/2
  5. 1

For the first problem, do not simply add the exponents together. You can only do that when you are multiplying exponents, not adding them. Instead, notice how there are 4 of the same number, 4^3. Therefore, 4^3(4^1)=4^4. Answer (C).

The next problem also asks you to add exponents, but first, you must multiply the exponents in parenthesis to the exponent outside the parenthesis, giving you: 2^20+2^6. Remember, that does not add up to 2^26. If you factor 2^6 from both 2^20 and 2^6, you get: 2^6*(2^14+1). Answer D. Also, you can use approximation and eliminate those answers that are too small and too big. Answer choice E is far too big, and Answer choice A too small.

For the last problem, the best way to deal with it is by plugging in the answer choices. B, C, and D will all result in some funky irrational number because you are taking the square or cube root of the number. That leaves us with (A) -1 and (E) 1. Plugging in (A), you end up getting 3^1+3^1+3^1=9. Therefore, the answer has to be (E) 1. Remember, also, that any number taken to a negative exponent results in the reciprocal of that number, e.g. 3^{-1}=1/3. And 1/3+1/3+1/3=1.

If you need more practice with exponents, look no further than Clemmonsdogpark – both our products (oh, yeah, did I mention – we just released our, over 600 practice questions waiting for you!) and on previous blog posts. Good luck!


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