Math 10 Exponents Practice Test

[Akinlolu Watters]

What about \(2^5*3^3\)? Well, the bases are different so we cannot combine them as we did before. Remember: you can only multiply exponential terms when the bases are the same. In this case, you would just have to multiply the long way, \(32*27=864\).

However (yup, just to make it a little more complicated!), there is one exception to this different base rule. If the exponents are the same but the base is different, you can multiply the bases. In \(2^5*3^5\), the bases are different but both are to the fifth power. In this case, we keep the power the same and we multiply the bases. Therefore, \(2^5*3^5=6^5\).

BUT, when the bases are different and the powers are the same, you can divide the bases. In \(4^5/2^5\), the bases are different but both are to the fifth power. In this case, we keep the power the same and we divide the bases. Therefore, \(4^5/2^5=2^5\).

Question 2
Answer: C. Do not simply add the powers together. You can only do that when you are multiplying powers, not adding them. Instead, notice how there are 4 of the same number, \(4^3\). Therefore, \(4^3(1+1+1+1) = 4^3(4) = 4^4 = 256\).

Question 3
Answer: E.The best way to deal with this problem 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 \(1/3+1/3+1/3=1\).

Question 4
Answer: B. Notice that \(4^10\) can be rewritten as \(2^20\). We can now express \(x\) as \(2^20 x 5^13\). The logic here is that \(2 x 5 = 10\). That is, 10 to any integer power greater than 1, will be a 1 followed by zeroes.

Go back up to Question 1.

Question 2
Answer: D First, you must multiply the power in parentheses to the power outside the parentheses, 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: \(2^6*(2^14+1)\). 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.

Lastly, for more GRE math practice (for exponents as well as other topics), try this full-length, free practice test from Magoosh that includes a detailed score report with a topic-by-topic breakdown of your performance. You can choose to do just the Quant section or a full length exam. Happy studying!

As for the other question, we basically want to find out when the two sides will be roughly equal. The first point at which the left side is smaller is the point we want as our answer. The strategy used was to try to get 4/5^n as close as possible to 1/2 so that it will be easier to work with.

So (4/5)^3 is a little larger than 1/2.
And (1/2)^4 = 1/16
Therefore, ((4/5)^3)^4 = (4/5)^12 = a little larger than 1/16
So, if we multiply by 4/5 one more time, we should get something less than 1/16. So instead of (4/5)^12, we take (4/5)^13.

Hi Abhishek! We have lots of exponents questions on our site if you have a premium account. As for additional free questions, there are a few in our free practice test, and of course any of the ETS materials ? ETS also collected links to relevant Khan Academy material, so I would check there as well: _general/prepare/khan_academy/

In this section, you can generate unlimited math practice tests. The key to mastering math is practice. Our practice tests and quizzes are great, but what happens when you need additional practice? Now, you can generate an unlimited number of unique practice tests. This way, you can continue to practice until you get it right.

A quick note on how this section works: When you take a practice test here, you must get 7 correct answers in order to pass. Once you have completed the practice test, you will see a trophy appear in the associated section. This trophy is saved via local storage. For most people, this will be enough, but keep in mind that your browser might not allow local storage, or this may get inadvertently cleared out. Best of luck in your studies, John.

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