Worksheet: Rules of Integer Powers

In this worksheet, we will practice solving problems involving operations on integers using the power rule.

Q1:

Simplify 4 × 2 5 2 × 5 0 .

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

Q2:

Simplify 1 4 𝑥 ÷ 7 𝑥 + 4 𝑥 , where 𝑥 0 .

  • A 6 𝑥
  • B 6 𝑥
  • C 1 1 𝑥
  • D 6 𝑥
  • E 1 1 𝑥

Q3:

What is the value of 2 2 ÷ 2 ?

Q4:

Given that 𝑧 = 1 4 , find the numerical value of ( 8 𝑧 ) × 𝑧 1 6 𝑧 .

  • A 1 8
  • B 4
  • C 1 3
  • D 1 1 2 8
  • E 6 4

Q5:

Simplify 4 5 × ( 6 3 ) × 3 2 2 5 × ( 2 1 ) .

  • A 3
  • B 9
  • C 3
  • D 3

Q6:

Simplify 2 × 3 0 2 × 6 × 5 .

  • A 5 6 , 9 1 2
  • B 6 , 9 1 2 5
  • C 2 1 6 5
  • D 5 2 1 6

Q7:

We can use the power rule of exponents applied to rational exponents to write 8 = 8 = 8 , × which simplifies to 8 , in the radical form 8 = 8 = 8 .

Use the example above to help you rewrite 2 3 in radical form.

  • A 2 3
  • B 2 3
  • C 2 3
  • D 2 3
  • E 6 9

Q8:

Find the value of 𝑎 for which 2 2 = 𝑎 × 2 .

Q9:

Given that 𝑧 = 1 3 , find the numerical value of ( 3 𝑧 ) × 𝑧 9 𝑧 .

  • A 1 1 8
  • B 1 9
  • C 1
  • D 9
  • E 3

Q10:

Given that 7 = 4 , find the value of 7 .

  • A 4 7
  • B 1 4
  • C 28
  • D 1 7
  • E 7 4

Q11:

Which of the following is true?

  • A 1 7 × 7 < 1
  • B 1 7 × 7 > 1
  • C 1 7 × 7 = 1

Q12:

Which of the following is true?

  • A 1 9 × ( 9 ) < 1
  • B 1 9 × ( 9 ) = 1
  • C 1 9 × ( 9 ) > 1

Q13:

Which of the following is true?

  • A 1 1 1 × ( 1 1 ) < 1 1
  • B 1 1 1 × ( 1 1 ) = 1 1
  • C 1 1 1 × ( 1 1 ) > 1 1

Q14:

Given that 2 = 3 , find the value of 2 .

Q15:

Calculate ( 4 ) ( 4 ) + ( 3 ) ( 3 ) .

Q16:

Calculate 3 3 + ( 3 ) .

Q17:

Calculate 2 + 2 2 .

Q18:

Fill in the blanks: ( 7 ) ( 7 ) 8 = .

Q19:

What is one-ninth of 9 ?

  • A 9
  • B1
  • C 9
  • D 9

Q20:

Calculate 8 8 + 8 8 + 8 8 + 8 .

Q21:

Which of the following is equal to 2 3 × 2 3 ?

  • A 3 2 2 4 3
  • B 4 0 9 6 5 3 1 4 4 1
  • C 6 4 7 2 9
  • D 4 9
  • E 2 4 5 4

Q22:

Which of the following expressions has the same value as 3 3 1 3 ?

  • A 1 0 0 3
  • B 1 0 0 3
  • C 1 0 0 3
  • D 1 0 0 3
  • E 1 0 0 3

Q23:

Which of the following has the same value as 1 1 2 ÷ 1 1 2 ?

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

Q24:

Which of the following expressions has the same value as 2 3 ?

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

Q25:

Which of the following is equal to 2 3 4 ?

  • A 5 1 2
  • B 2 2 8
  • C 2 9 1 6
  • D 4 9 1 6
  • E 7 9 1 6

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