# SAT Math Multiple Choice Question 747: Answer and Explanation

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**Question: 747**

**12.** If *n* is a positive integer and *m* = 2^{n} ^{+} ^{2} + 2^{n}, what is 2^{n} ^{+} ^{3} in terms of *m*?

- A.
*m* - B.
- C.
- D. 3
*m*^{2}

**Correct Answer:** C

**Explanation:**

**C**

**Advanced Mathematics (exponentials) HARD**

Notice that this question asks us to find the value of 2^{n +3}, so we should try to solve the given equation for 2^{n +3}.

Original equation:

*m* = 2^{n + 2} + 2^{n}

Factor 2*n* from the terms on the right side:

*m* = 2^{n} (2^{2} + 1)

Simplify:

*m* = 2^{n} (5)

Divide by 5:

Multiply by 2^{3} :

Simplify: