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# Tip #31 to Get a Top ACT Math Score

By Brian Leaf
McGraw-Hill Professional

I fear that I will always be

A lonely number like root three.

A three is all that's good and right,

Why must my three keep out of sight?

Beneath a vicious square root sign,

I wish instead I were a nine …

Kumar Patel, Harold & Kumar Escape from Guantanamo Bay (Warner Bros., 2008)

2n2 + n2 = 3n2               When adding with matching bases and matching exponents, add coefficients.

2n + n2                           Does not combine. When adding, they combine only if they have matching bases and matching coefficients.

n–2 =                     A negative exponent means "take the reciprocal."

N4/3 =                   For a fractional exponent, the top number is the power and the bottom number is the root.

Let's take a look at this question:

Solution: Great review of Skill 3. "What is m in terms of p" means "solve for m—use algebra to get m alone."

8m2p3 = m5p                     Divide both sides by p.

8m2p2 = m5                     Divide both sides by m2.

8p2 = m3                     Put both sides to the one-third exponent, since (m3)1/3 = m

(8p2)1/3 = m                     Distribute the exponent.

2p2/3 = m

### Easy

1. What is the sum of 2x2 and 2x3 ?
1. 4x5
2. 2x6
3. 2x2 + 2x3
4. 2x4 + 2x4
5. (2x2)(2x3)

### Medium

1. The product of 3m–2 and 2m–5 is

### Hard

1. For positive real numbers a, b, and c, which of the following expressions is equivalent to a2/3b1/6c1/2 ?
2. If , then x = ?
1. 2
2. 1
3. 0
1. –1
2. –2

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