Worksheet: Fractional Exponents

In this worksheet, we will practice simplifying fractional exponents and converting between exponential and radical expressions.

Q1:

Simplify 364×136×(16).

Q2:

Express 𝑥 in the form 𝑎.

  • A 𝑥
  • B 𝑥
  • C 𝑥
  • D 𝑥

Q3:

Evaluate 125343.

  • A 2 5 7
  • B 5 7
  • C 2 5 4 9
  • D 7 2 5
  • E 5 4 9

Q4:

Evaluate 243.

Q5:

When exponents are written as decimals, they can be converted to fractions: 11=11.

This makes it easier to write the expressions in radical form: 11=11.

Now, write 7 in radical form.

  • A 5
  • B 7
  • C 7
  • D 7
  • E 5

Q6:

Write 11 in radical form.

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

Q7:

Evaluate 100,000.

Q8:

Evaluate 3,125.

Q9:

3 2 = 3 2 = 3 2 × 3 2 × 3 2 = 3 2 = 2 = 8 .

In general, 𝑎 means the 𝑥th exponent of the 𝑦th root of 𝑎. So, 32 means “the fifth root of 32, cubed”.

Evaluate 16.

Q10:

Evaluate 256.

Q11:

8 1 = 8 1 = 8 1 = ( 3 ) = 2 7 .

In this example we could see that 0.75 is equivalent to 34 so we need to calculate the cube of the fourth root of 81.

Evaluate 16.

Q12:

2 1 6 = 2 1 6 = 2 1 6 = 2 1 6 × 2 1 6 × 2 1 6 = 2 1 6 × 2 1 6 × 2 1 6 .

This is an example of using rational exponents to represent radicals. So, 216 means “the cube root of 216” or 216.

Evaluate 27.

Q13:

Evaluate 243.

Q14:

Evaluate 64.

Q15:

Evaluate 256.

Q16:

Completely simplify 5.0625.

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

Q17:

Evaluate 100,000.

Q18:

Evaluate 64.

Q19:

Evaluate 32.

Q20:

Evaluate (0.0625).

  • A 1 6 4
  • B 1 8 0
  • C 1 4
  • D 1 2
  • E 5 1 6

Q21:

4 9 = 4 9 = 4 9 = 4 9 = 4 9 × . This is an example of using rational exponents to represent radicals. So, 49 means “the square root of 49” or 7.

Evaluate 25.

Q22:

𝑎 𝑏 means the 𝑐th exponent of the 𝑑th root of 𝑎𝑏. In the example shown, we can evaluate the numerator and denominator separately.

8 2 7 = 8 2 7 = 8 2 7 = 2 3 = 4 9 .

Evaluate 32243.

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

Q23:

4 9 = 4 9 = 4 9 × 4 9 = 4 9 × 4 9 . This is an example of using rational exponents to represent radicals. So, 49 means “the square root of 49” or 49.

Evaluate 16.

Q24:

Which of the following is equal to 9?

  • A 8 1
  • B 9
  • C 9 2
  • D 8 . 5
  • E 1 8

Q25:

Which of the following expressions is equivalent to 13×13×13?

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

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