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.

  • A𝑥
  • B𝑥
  • C𝑥
  • D𝑥

Q3:

Evaluate 125343.

  • A257
  • B57
  • C2549
  • D725
  • E549

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.

  • A5
  • B7
  • C7
  • D7
  • E5

Q6:

Write 11 in radical form.

  • A11
  • B11
  • C11
  • D19
  • E11

Q7:

Evaluate 100,000.

Q8:

Evaluate 3,125.

Q9:

32=32=32×32×32=32=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:

81=81=81=(3)=27.

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:

216=216=216=216×216×216=216×216×216.

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.

  • A278
  • B32
  • C818
  • D272
  • E38

Q17:

Evaluate 100,000.

Q18:

Evaluate 64.

Q19:

Evaluate 32.

Q20:

Evaluate (0.0625).

  • A164
  • B180
  • C14
  • D12
  • E516

Q21:

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

Evaluate 25.

Q22:

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

827=827=827=23=49.

Evaluate 32243.

  • A23
  • B83
  • C827
  • D227
  • E8243

Q23:

49=49=49×49=49×49. 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?

  • A81
  • B9
  • C92
  • D8.5
  • E18

Q25:

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

  • A13
  • B13
  • C39
  • D13
  • E39

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