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
- 2x2 · 3x3y · 3x3y is equivalent to
- What is the product of m3 and 2m5 and ?
- 2m15 – m2
- If x is a real number such that x3 = 27, then x3 + x2 = ?
- Which of the following expressions is equivalent to (–3x3y4)4 ?
- If it travels at 186,000 miles per second, about how many miles does a ray of light travel in 3 hours?
- 2 × 108
- 2 × 109
- 3 × 1010
- 3 × 1011
- 4 × 1012
- If m, n, and p are positive integers such that mp = x and np = y, then xy = ?
- 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.
- 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
- 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.
- K (–3x3y4)4 = (–3)4(x3)4(y4)4 = 81x12y16. Careless Error Buster: Remember that the (–3) also gets the exponent.
- 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.
- 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
Washington Virtual Academies
Tuition-free online school for Washington students.
- Coats and Car Seats: A Lethal Combination?
- Kindergarten Sight Words List
- Signs Your Child Might Have Asperger's Syndrome
- Child Development Theories
- GED Math Practice Test 1
- 10 Fun Activities for Children with Autism
- Social Cognitive Theory
- Why is Play Important? Social and Emotional Development, Physical Development, Creative Development
- The Homework Debate
- Problems With Standardized Testing