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Positive Exponents

  • To evaluate a base raised to an exponent, multiply the base or factor the number of times indicated by the exponent.
  • The order of operations:
  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Subtraction (left to right)
  • An exponent applies only to its base, so ( −4 )2 = 16 but −42 = −16.

Write 7 · 7 · 7 · 7 · 5 · 5 using exponents.

  • There are four 7s and two 5s.

74 ·52

Write 5 · 5 · 5 · ( - 2) · ( - 2) · ( - 2) · ( - 2) using exponents.

  • There are three 5s and four (-2)s.

53 ·( − 2)4

Write m · m · p · p · p · ( - 4) · ( - 4) using exponents .

  • There are two ms, three ps, and two ( - 4)s.

m2 ·p3 ·( − 4)2

Compare ( − 5)4 to - 54.

  • ( − 5)4 = ( − 5) ·( − 5) ·( − 5) ·( − 5) =
  • 25 ·25 =
  • 625
  • − 54 = − 5 ·5 ·5 ·5 =
  • − 25 ·25 =

- 625

Evaluate (5 ·m)2 − 7 for m = 2

  • (5 ·2)2 − 7 =
  • 102 − 7 =
  • 100 − 7 =

93

Evaluate (3y − 5)2 + 2y for y = 6

  • (3(6) − 5)2 + 2(6) =
  • (18 − 5)2 + 12 =
  • (3)2 + 12 =
  • 9 + 12 =

21

Evaluate (2r − s)2 + 3s for r = 6 and s = 2.

  • (2(6) − 2)2 + 3(2) =
  • (12 − 2)2 + 3(2) =
  • 102 + 6 =
  • 100 + 6 =

106

Evaluate (x − 3y)3 + (4 − z)2 for x = 4, y = 2, and z = 2.

  • (4 − 3(2))3 + (4 − 2)2 =
  • (4 − 6)3 + (4 − 2)2 =
  • (−2)3 + (2)2 =
  • ( − 2) ·( − 2) ·( − 2) + 2 ·2 =

- 32

The formula h = 160t − t2 is used to estimate the number of feet a ball rises in t seconds after it is thrown. How high is a ball 3 seconds after it is thrown?

  • h = 160t − t2, t = 3 feet
  • h = 160(3) − 32 feet
  • h = 480 − 9 feet

h = 371 feet

A certain type of bacteria doubles in population every 6 hours. Given that there were 10 bacteria to begin with, how many bacteria will there be after one day, assuming all of them stay alive?

  • One day has 24 hours.
  • After 6 hours, the bacteria population will be 10 × 2 bacteria.
  • After 12 hours, the bacteria population will be 10 ×2 ×2 = 10 ×22 bacteria.
  • After 18 hours, the bacteria population will be 10 ×2 ×2 ×2 = 10 ×23 bacteria.
  • After 24 hours, the bacteria population will be 10 ×2 ×2 ×2 ×2 = 10 ×24 bacteria.
  • 10 ×24 =
  • 10 ×16 =

160 bacteria

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Positive Exponents

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Mathematics: Pre Algebra

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