Worksheet: Exponential Expressions to Radical Expressions

In this worksheet, we will practice converting an exponential expression to its equivalent radical form.

Q1:

Write 7 × 7 5 1 2 3 1 2 in radical form.

  • A 7 1 2 1 5
  • B 7 2 3
  • C 7 8 1 2
  • D 7 3 2
  • E 1 4 1 2 8

Q2:

Write 6 × 6 2 3 6 8 in radical form.

  • A 6 1 1 8
  • B 6 1 7 1 2
  • C 3 6 1 2 1 7
  • D 6 1 2 1 7
  • E 1 2 1 1 8

Q3:

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

Q4:

Express 𝑥 × 𝑥 in the form 𝑎 .

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥
  • E 𝑥

Q5:

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

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

  • A 4 1 5 9
  • B 4 5 3
  • C 1 6 8 1 5 6
  • D 4 3 5
  • E 8 3 5

Q6:

Which of the following is equivalent to 6 4 ?

  • A 6 4
  • B 6 4
  • C 6 4 6 4
  • D 6 4
  • E 6

Q7:

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

  • A 3 2 3 5
  • B 3 2 3
  • C 3 2 3 2 3 5
  • D 3 2 5 3
  • E 3 5 3 2

Q8:

Remember that 8 = 8 = ( 2 ) = 4 2 3 3 2 2 .

Also, 8 = 8 = 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 3 4 1 6
  • B 1 6 3 4
  • C 1 6 3 4
  • D 4 1 6 3
  • E 4 3 1 6

Q9:

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

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

Q10:

Calculate 1 4 9 .

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

Q11:

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 ) 3 4 .

Q12:

Completely simplify 6 4 1 2 5 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

Q13:

Evaluate 3 1 3 8 1 .

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

Q14:

Completely simplify 8 1 1 0 0 0 0 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

Q15:

Remember that and

So, for example,

Use the example above to help you simplify 3 2 1 0 0 0 0 0 2 5 .

Q16:

Write 6 | | 𝑥 | | 𝑦 as a radical expression.

  • A 2 𝑥 𝑦
  • B 6 𝑥 𝑦
  • C 3 6 𝑥 𝑦
  • D 3 6 𝑥 𝑦
  • E 1 2 𝑥 𝑦

Q17:

Express 𝑥 × 𝑥 in the form 𝑎 .

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥
  • E 𝑥

Q18:

Express 𝑥 × 𝑥 in the form 𝑎 .

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥
  • E 𝑥

Q19:

Express 𝑥 × 𝑥 in the form 𝑎 .

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥
  • E 𝑥

Q20:

Express 𝑥 × 𝑥 in the form 𝑎 .

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥
  • E 𝑥

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.