Tip #30 to Get a Top ACT Math Score (page 2)

The ACT loves to test the laws of exponents. I know that you think that the ACT is incapable of love, that they are a sadistic organization. But I've visited their building, camped outside, and walked among them, and I can tell you that they are almost normal people.

Anyway, the ACT loves exponents; they are on every test. Memorize these rules. Practice working with them in the drills, and check your answers. Then teach them to a friend.

n⁶ × n² = n⁸     When multiplying matching bases, add exponents.

    When dividing matching bases, subtract exponents.

(n⁶)² = n¹²     Power to a power, multiply exponents.

n⁰ = 1     Any base to the 0 power equals 1.

Let's look at this question:

Solution: (–2x²y²)³ = (–2) ³ (x²) ³ (y²)³ = –8x⁶y⁶.

Correct answer: G

Example Problems

Easy

1. 2x² · 3x³y · 3x³y is equivalent to
   1. 8x⁸y²
   2. 8x¹⁸y²
   3. 18x⁸y
   4. 18x¹⁸y²
   5. 18x⁸y²
2. What is the product of m³ and 2m₅ and ?
   6. 2m¹³
   7. 2m⁶
   8. 3m¹³
   10. 4m⁶
   11. 2m₁₅ – m₂
3. If x is a real number such that x³ = 27, then x³ + x² = ?
   1. 27
   2. 29
   3. 32
   4. 36
   5. 42

Medium

4. Which of the following expressions is equivalent to (–3x³y⁴)⁴ ?
   6. –27x⁷y⁸
   7. –81x¹²y¹⁶
   8. 27x⁷y⁸
   10. 81x⁷y⁸
   11. 81x¹²y¹⁶
5. If it travels at 186,000 miles per second, about how many miles does a ray of light travel in 3 hours?
   1. 2 × 10₈
   2. 2 × 10⁹
   3. 3 × 10¹⁰
   4. 3 × 10¹¹
   5. 4 × 10¹²
6. If m, n, and p are positive integers such that m^p = x and n^p = y, then xy = ?
   1. mn^p
   2. (mn2)^p
   3. (mn)^p
   10. (mn)^2p
   11. (mn)^p2