Which of the following is equal to x^18 for all positive values of x ?

Certainly (B) for the reasons cited by the users above.

Asked: Which of the following is equal to \(x^{18}\) for all positive values of x ?


A. \(x^9 + x^9\)
2x^9
B. \((x^2)^9\)
x^18
C. \((x^9)^9\)
x^81
D. \((x^3)^{15}\)
x^45
E. \(\frac{x^4}{x^{22}}\)
x^{-18}

IMO B

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Answer choice B , for all positive values of X

Solution:

Since (x^2)^9 = x^(2 * 9) = x^18, choice B is the correct answer.

Answer: B

This is certainly an easy one IF you know your exponents rules (WHICH YOU SHOULD!!!). But let's say you totally blank out on the actual test and forget the rules. You can still get this one right by figuring out the rule using a simpler example. Instead of \(x^{18}\), just do something like \(2^{6}\) and see if you can figure out what's up.

x=2

\(2^{4} = 64\)

We can see in the answer choices that there are some 9's. That's half of the 18 from the question stem. We replaced the 18 with a 6, so every time there's a 9 in an answer choice, we need to replace it with half of 6, so 3.

A. \(2^3 + 2^3 = 8+8 = 16\) ... Nope.

B. \((2^2)^3 = 4^3 = 64\) ... Keep it.

C. \((2^3)^3 = 6^3\) ... 6^3 can't be equal to 4^3 and 4^3 worked, so 6^3 can't. Nope.

D. \((2^3)^{15}\) ... Woah. Huge. Nope.

E. \(\frac{2^4}{2^{22}}\) ... Less than 1? Nope.

Answer choice B.

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