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Worksheet: Powers and Exponents

In this worksheet, we will practice identifying the base and exponent in power formulas, writing them in exponential, expanded and word forms, and evaluating simple powers.

Q1:

Find the value of ( − 3 ) × 3 3 2 3 .

Q2:

Calculate × 1 2 7 1 2 2 1 2 3 , giving your answer in its simplest form.

  • A 1 2 5 6
  • B 64
  • C 256
  • D 1 6 4

Q3:

Find the value of 5 2 .

Q4:

What terminology do we use to describe the 3 in the term 𝑥 3 ?

  • Aan expression
  • Ba base
  • Ca factor
  • Dan exponent
  • Ea coefficient

Q5:

Is the following correct: 6 = 2 × 2 × 2 × 3 × 3 × 3 3 ?

  • A yes
  • B no

Q6:

Evaluate 5 1 .

Q7:

Calculate 2 × 2 × 3 × 3 7 4 2 3 .

Q8:

Simplify − 1 2 𝑥 𝑦 6 𝑥 𝑦 6 5 4 .

  • A − 2 𝑥 𝑦 6 5
  • B − 2 𝑥 𝑦 1 0 6
  • C − 2
  • D − 2 𝑥 𝑦 2 4

Q9:

Write four squared using digits.

  • A 4 3
  • B 3 4
  • C 2 4
  • D 4 2

Q10:

Write the expression 3 4 in words.

  • Athree to the fifth power
  • Bfour to the three power
  • Cfour to the fourth power
  • Dthree to the fourth power

Q11:

What is the base in 5 7 ?

Q12:

Is the following correct: 3 = 3 + 3 + 3 + 3 4 ?

  • A no
  • B yes

Q13:

Write seven to the fourth power using digits.

  • A 4 7
  • B 7 5
  • C 5 7
  • D 7 4

Q14:

The cost of each flight of the space shuttle is about $ 1 0 0 0 0 0 0 0 . Write this cost in exponential form.

  • A 1 0 8 dollars
  • B 1 0 6 dollars
  • C 1 0 0 5 dollars
  • D 1 0 7 dollars
  • E 1 0 0 6 dollars

Q15:

The African bush elephant is the largest land animal and weighs about 8 tons. Express this amount in exponential form.

  • A 4 2 tons
  • B 3 2 tons
  • C 2 4 tons
  • D 2 3 tons
  • E 2 6 tons

Q16:

Express the volume of a cube of edge length 32 units as an exponent, and then determine its value.

  • A 3 3 2 , 32 768 cubic units
  • B 3 2 3 , 96 cubic units
  • C 2 3 2 , 64 cubic units
  • D 3 2 3 , 32 768 cubic units
  • E 3 2 2 , 1 024 cubic units

Q17:

The prefix kilo in kilometre represents 1 0 0 0 metres. Write this length as a power of ten.

  • A 1 0 1 2 metres
  • B 1 0 9 metres
  • C 1 0 6 metres
  • D 1 0 3 metres
  • E 1 0 8 metres

Q18:

The prefix mega in megameter represents metres. Write this number as a power of ten.

  • A
  • B
  • C
  • D
  • E

Q19:

Find the digit in the units place of 5 × 2 4 6 .

Q20:

Use a calculator to determine whether this sentence is true or false: 2 < 4 4 2 .

  • Afalse
  • Btrue

Q21:

Complete the following using < , > , or = : 3 3 3 5 .

  • A =
  • B >
  • C <

Q22:

Complete the following using < , > , or = : 8 2 2 6 .

  • A >
  • B <
  • C =

Q23:

Which of the following is true?

  • A 5 > 1 2 5 3
  • B 5 < 1 2 5 3
  • C 5 = 1 2 5 3

Q24:

Complete the following using < , > , or = : 4 3 5 5 .

  • A =
  • B <
  • C >

Q25:

Complete the following using < , > , or = : 4 6 3 2 .

  • A =
  • B <
  • C >

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