Exponents Negative Exponents Product of Powers Law Quotient of Powers Law Identify number sets Order numbers in the real number system

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Hour ________________

1 Topics to Know:  Exponents

 Negative Exponents

 Product of Powers Law

 Quotient of Powers Law

 Identify number sets

 Order numbers in the real number system

 Convert between scientific notation and standard form

 Compute with scientific notation

 Square roots

 Cube roots

SHOW YOUR WORK!

1. Write the expression using exponents. (4.1) 8  8  𝑐  𝑐  𝑐  𝑐  𝑑  𝑑  𝑑

2. Write the expression using a positive exponent. (4.2)

(−2)⁻⁶

3. Find the product. Express using positive exponents. (4.3)

(6𝑏³)(3𝑏⁴)

4. Find the quotient. Express using positive exponents. (4.3)

12𝑞⁴ 6𝑞²

5. Express the number in standard form. (4.4) 6.78 × 10⁸

6. Finish the inequality using <, >, or = to make the statement true. (4.4)

8.8 × 10³ ● 9.1 × 10⁻⁴

7. Evaluate the expression. Express the result in scientific notation. (4.5)

(3.2 × 10⁴)(1.4 × 10²)

(7.2 × 10⁶) + (1.25 × 10⁵)

9. Find the square root. (4.6)

±√289

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2 10. Find the cube root. (4.6)

√2197

3

11. Name all sets of numbers to which the real number belongs. Write ℕ (natural), 𝕎 (whole), ℤ (integer), ℚ (rational), or irrational. (4.7)

0.050050005 …

7.8 ● √55

13. Evaluate the expression if 𝑎 = −3, 𝑏 = 8, and 𝑐 = 2. (4.1)

(𝑏 − 𝑐)²

14. Evaluate the expression if 𝑥 = 1, 𝑦 = 2, and 𝑧 = −3. (4.2)

𝑦⁻⁵

15. The product of two squared and two to the sixth power. (4.3)

7⁹ 7⁶

17. Express the number in scientific notation.

(4.4)

0.0054

18. Order the set of numbers from least to greatest. (4.4)

3.6 × 10⁴, 5.8 × 10⁻³, 2.1 × 10⁶, 3.5 × 10⁵

4.55 × 10⁷ 1.3 × 10⁴

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3 20. Evaluate the expression. Express the result in

scientific notation. (4.5)

(8.4 × 10⁵) − (7.9 × 10³)

21. Estimate the square root to the nearest tenth.

(4.6)

−√19

22. Estimate the cube root to the nearest tenth.

(4.6)

√−736

3

−32 4

51

3, 5.3, √28, 21 4

25. Write the expression using exponents. (4.1) (−𝑤)(−𝑤)(𝑣)(𝑣)(𝑣)(𝑣)(𝑣)

26. Write the expression using a negative exponent. (4.2)

1 𝑏⁸

11𝑎² 3𝑎⁻⁶

28. The quotient of a to the twentieth power and a to the tenth power. (4.3)

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4 29. Express the number in standard form. (4.4)

8.075 × 10⁻⁴

5.01 × 10² ● 5.02 × 10⁻¹

31. IF each of the 3 × 10⁴ people employed by Sunny Motors earned 4 × 10⁴ dollars last year, how much money did the company pay out to its employees?

32. Evaluate the expression. Express in scientific notation. (4.5)

(7.85 × 10⁵) + (4.78 × 10⁴)

√−81

34. Find the cube root. (4.6)

√−1331

3

24.6

√4 ● 23 7

𝑏²+ 𝑎³

4^𝑧

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5 39. Find the product. Express using positive

exponents. (4.3)

(−𝑣)⁻³(−𝑣)⁷

21𝑡¹⁹ 3𝑡¹²

(4.4)

803,000

64,000,000; 6.2 × 10⁻³, 6,400,000; 6.4 × 10⁵

(4.3 × 10⁻²)(5.6 × 10⁻⁴)

(6.5 × 10¹²) + (3.1 × 10¹¹)

(4.6)

−√119

(4.6)

√2698

3

√31

−9.35, −√72.75, −9 2 10, −9

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6 49. Write the expression using exponents. (4.1)

𝑟  𝑟  𝑟  𝑡  𝑢  𝑢  𝑟

50. Write the expression using a positive exponent. (4.2)

𝑣⁻¹¹

(𝑝⁴)(𝑝⁴)

𝑞⁴ 𝑞⁸

53. Express the number in standard form. (4.4) 3.0005 × 10⁵

8.4 × 10² ● 839

1.175 × 10⁻³ 1.25 × 10⁻⁶

(9.2 × 10³) − (9.6 × 10²)

√625

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7 58. Find the cube root. (4.6)

√8000

3

25 3

15.1 ● √231

𝑐³  3^𝑐

𝑦^−𝑧

63. The product of y squared and y cubed. (4.3)

100𝑟⁵ 10𝑟⁸

(4.4)

0.000099

0.00048, 4.37 × 10⁻⁴, 4.02 × 10⁻³, 0.04

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8 67. The distance from Earth to the Moon is about

2 × 10⁵ miles. The distance from Earth to the Sun is about 9.3 × 10⁷ miles. How many times farther is it to the Sun than to the Moon? (4.5)

(9.43 × 10⁹) − (6.84 × 10⁶)

(4.6)

±√83

(4.6)

√−611

3

0

√53, 71 4,36

5 , 7.27