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

By McGraw-Hill Professional
Updated on Sep 7, 2011

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

### 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 ?
1. 2m13
2. 2m6
3. 3m13
1. 4m6
2. 2m15m2
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

1. Which of the following expressions is equivalent to (–3x3y4)4 ?
1. –27x7y8
2. –81x12y16
3. 27x7y8
1. 81x7y8
2. 81x12y16
2. 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
3. If m, n, and p are positive integers such that mp = x and np = y, then xy = ?
1. mnp
2. (mn2)p
3. (mn)p
1. (mn)2p
2. (mn)p2

### Answers

1. E Multiply coefficients (numbers in front of the letters) and add exponents. So 2x2 · 3x3y · 3x3y = (2 · 3 · 3)(x2+3+3)(y1+1) = 18x8y2. Remember that y really means y1.
2. G When you multiply variables, like m, you add the exponents; and when you divide m's, you subtract the exponents. So, m3 × 2m5 × IMG
3. D Springboard review: when you see something that can simplified, do it. x3 = 27 simplifies to x = 3, since 33 = 27. Then just plug 3 in for each x: 33 + 32 = 27 + 9 = 36.
4. K (–3x3y4)4 = (–3)4(x3)4(y4)4 = 81x12y16. Careless Error Buster: Remember that the (–3) also gets the exponent.
5. B 186,000 is in miles per second. To get miles per minute, multiply by 60. And then to get miles per hour, multiply by 60 again. Finally, to get 3 hours, multiply by 3: 186,000 × 60 × 60 × 3 = 2,008,800,000. Then just type each answer choice into your calculator to see which one matches best. Choice B, 2,000,000,000, is closest. A number written in the form 2 × 109 is called scientific notation, and just means 2 with 9 zeros, or 2,000,000,000. So even if a number in scientific notation was too big for your calculator, just remember that it means the first number with as many zeros as the number in the exponent, like 5 × 104 = 50,000.
6. H Since mp = x and np = y, then xy = (mp)(np) = (mn)p. Notice that this time I did not add the exponents because m and n are different letters, and we only add exponents when the base is the same.

Go to: Tip #31

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