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Worksheet: Converting Exponential Expressions to Radical Expressions and Simplifying Them

Q1:

Express π‘₯ Γ— π‘₯ 1 6 3 2 3 2 in the form π‘š √ π‘Ž 𝑛 .

  • A √ π‘₯ 1 0 1
  • B 1 0 1 √ π‘₯ 6
  • C 6 √ π‘₯
  • D 6 √ π‘₯ 1 0 1
  • E 3 √ π‘₯ 1 8 4

Q2:

Express π‘₯ Γ— π‘₯ 2 3 1 3 1 8 in the form π‘š √ π‘Ž 𝑛 .

  • A √ π‘₯ 2 5
  • B 2 5 √ π‘₯ 1 8
  • C 1 8 √ π‘₯
  • D 1 8 √ π‘₯ 2 5
  • E 2 7 √ π‘₯ 1 3

Q3:

Using the addition rule for rational exponents, we can write in the radical form

Use the example above to help you rewrite 4 Γ— 4 7 9 8 9 in radical form.

  • A ο€» √ 4  1 5 9
  • B ο€» √ 4  5 3
  • C ο€» √ 1 6  8 1 5 6
  • D ο€» √ 4  3 5
  • E ο€» √ 8  3 5

Q4:

Express π‘₯ Γ— π‘₯ 9 2 0 1 9 8 in the form π‘š √ π‘Ž 𝑛 .

  • A √ π‘₯ 1 1 3
  • B 1 1 3 √ π‘₯ 4 0
  • C 4 0 √ π‘₯
  • D 4 0 √ π‘₯ 1 1 3
  • E 1 6 0 √ π‘₯ 1 7 1

Q5:

Express π‘₯ Γ— π‘₯ 1 2 2 0 4 3 in the form π‘š √ π‘Ž 𝑛 .

  • A √ π‘₯ 8 3
  • B 8 3 √ π‘₯ 8 6
  • C 8 6 √ π‘₯
  • D 8 6 √ π‘₯ 8 3
  • E 4 3 √ π‘₯ 1 0

Q6:

Express π‘₯ Γ— π‘₯ 1 1 2 1 9 1 8 in the form π‘š √ π‘Ž 𝑛 .

  • A √ π‘₯ 5 9
  • B 5 9 √ π‘₯ 9
  • C 9 √ π‘₯
  • D 9 √ π‘₯ 5 9
  • E 3 6 √ π‘₯ 2 0 9

Q7:

Write 7 Γ— 7 5 1 2 3 1 2 in radical form.

  • A ο€» √ 7  1 2 1 5
  • B ο€» √ 7  2 3
  • C ο€» √ 7  8 1 2
  • D ο€» √ 7  3 2
  • E ο€» √ 1 4  1 2 8

Q8:

Write 6 Γ— 6 2 3 6 8 in radical form.

  • A ο€» √ 6  1 1 8
  • B ο€» √ 6  1 7 1 2
  • C ο€» √ 3 6  1 2 1 7
  • D ο€» √ 6  1 2 1 7
  • E ο€» √ 1 2  1 1 8

Q9:

A square has an area of 349 cm2. Determine the length of its diagonal.

  • A √ 1 7 4 . 5 cm
  • B √ 3 4 9 cm
  • C 174.5 cm
  • D √ 6 9 8 cm
  • E 87.25 cm

Q10:

Which of the following is equivalent to ?

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the following is equivalent to 3 2 3 5 ?

  • A ο€» √ 3 2  3 5
  • B ο€» √ 3 2  3
  • C 3 2 3 2 3 5
  • D ο€» √ 3 2  5 3
  • E 3 √ 5 3 2

Q12:

Remember that 8 = ο€» √ 8  = ( 2 ) = 4 2 3 3 2 2 .

Also, 8 = ο€» √ 8  = ο€» √ 6 4  = 4 2 3 3 3 2 .

The first method is easier to calculate.

Which of the following is equivalent to 1 6 3 4 ?

  • A ο€» √ 3  4 1 6
  • B ο€» √ 1 6  3 4
  • C ο€» √ 1 6  3 4
  • D 4 √ 1 6 3
  • E ο€» √ 4  3 1 6

Q13:

Which of the following is equivalent to 6 4 1 3 ?

  • A ο€» √ 6 4  3
  • B √ 6 4
  • C 1 6 4 3
  • D 3 √ 6 4
  • E 3 √ 6 4 3

Q14:

Calculate ο€Ό 1 4 9  1 2 .

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

Q15:

Remember that and that converting decimal bases to top heavy fractions can help you to simplify expressions with exponents.

For example,

Use the example above to help you simplify ( 0 . 0 0 1 6 ) βˆ’ 3 4 .

Q16:

Completely simplify ο€Ό 6 4 1 2 5  βˆ’ 5 3 .

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

Q17:

Evaluate .

  • A
  • B
  • C
  • D
  • E

Q18:

Completely simplify ο€Ό 8 1 1 0 0 0 0  βˆ’ 5 4 .

  • A 1 0 0 0 0 2 4 3
  • B 2 4 3 1 0 0 0 0 0
  • C 1 0 2 4 3
  • D 1 0 0 0 0 0 2 4 3
  • E 1 0 0 0 0 0 3

Q19:

Remember that and

So, for example,

Use the example above to help you simplify ο€Ό 3 2 1 0 0 0 0 0  βˆ’ 2 5 .

Q20:

Write 6 | | π‘₯ | | 𝑦 9 1 2 as a radical expression.

  • A √ 2 π‘₯ 𝑦 4 6
  • B √ 6 π‘₯ 𝑦 1 8 2 4
  • C √ 3 6 π‘₯ 𝑦 9 1 2
  • D √ 3 6 π‘₯ 𝑦 1 8 2 4
  • E √ 1 2 π‘₯ 𝑦 1 8 2 4