C4a
Practice - Exponents
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. Evaluate 3³ + 4⁴.
2. Simplify 2 ²+ 4 ² - 2 ² - (4 - 2) ².
3. What is 14⁰ ? What is x⁰ ?
4. What is 1⁹?
5. A cube measures 6 inches on each side. The built-in formula sheet says that the volume of the cube is equal to the cube of the side. What is the volume of this cube?
6. What is 4 ⁷?
7. Which is the least: (a) (1/3)³ , (b) 4 ⁰ , (c) 4¹ , (d) 1/2)⁴ ?
ANSWERS
1. 3 is 3x3x3 = 27. 4 is 4x4x4x4 = 256. 27 + 256 = 283.
2. This is mostly about² the order of operations. First combine (4 - 2) to get 2. Then notice that 2² appears three times, and that the algebraic sum of these three terms is 2 - 2 - 2, or -2. So you have 4² - 2², or 16 - 4 = 12. If the test's built-in calculator were available, you could enter the entire expression directly and read the answer. As you enter an expression like this, be careful to get the parentheses right.
3. One. Anything to the zero power is one.
4. 1. 1 to any power is still equal to 1.
5. The volume equals 6³ . This is 216, which you can find by multiplying 6 x 6 x 6 manually (or with the test's built-in calculator if it is available).
6. It is 4x4x4x4x4x4x4 = 16,384. You could do this directly on the built-in calculator, if it is available.
7. (a) (1/3)³ = (1/3) x (1/3) x (1/3) = 1/9. (b) 4⁰ = 1. (c) 4¹ = 4. (d) (1/2)⁴ = (1.2) x (1/2) x (1/2) x (1/2) = 1/16. The answer is (d).
CALCULATOR STEPS
In addition to the calculator keys used in the preceding pages, this page uses the "x²" key and the "exp" key. (The exp key looks like an upside-down v, and is directly above the x² key.)
1. Press on and clear. Key in 3. Press exp. Key in 3. Press right. Press + . Key in 4. Press exp. Key in 4. Press enter. The screen should show "283".
2. Press on and clear. Key in 2. Press x². Press + . Key in 4. Press x². Press - . Key in 2. Press x² . Press - . Press ( . Key in 4. Press - . Key in 2. Press ) . Press x² . Press enter. The screen should show "12".
3. The calculator is not useful. Anything to the zero power is 1.
4. The calculator is not useful. 1 to any power is still 1.
5. Press on and clear. Key in 6. Press exp. Key in 3. Press enter. The screen should show "216".
6. Press on and clear. Key in 4. Press exp. Key in 7. Press enter. The screen should show "16384".
7. Press on and clear. Press n/d. Key in 1. Press down. Key in 3. Press right. Press exp. Key in 3. Press enter. The screen should show "1/27". Press <> . The screen should show "0.037...". Press clear. Key in 4. Press exp. Key in 0. Press enter. The screen should show "1". Press clear. Key in 4. Press exp. Key in 1. Press enter. The screen should show "4". Press clear. Press n/d. Key in 1. Press down. Key in 2. Press right. Press exp. Key in 4. Press enter. The screen should show "1/16". Press <> . The screen should show "0.0625". The first option is the least.
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