Lesson: Fractional Exponents

In this lesson, we will learn how to simplify fractional indices.

Video

14:38

Sample Question Videos

  • 01:58
  • 00:57

Worksheet: Fractional Exponents • 25 Questions • 2 Videos

Q1:

Simplify 3 6 4 Γ— ο€Ό 1 3 6  Γ— ( 1 6 ) 1 2 1 2 .

Q2:

Express π‘₯ 1 9 3 in the form π‘š √ π‘Ž 𝑛 .

Q3:

Evaluate ο€Ό 1 2 5 3 4 3  2 3 .

Q4:

Evaluate 2 4 3 3 5 .

Q5:

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

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

Now, write 7 2 . 6 in radical form.

Q6:

Write 1 1 3 . 8 in radical form.

Q7:

Evaluate 1 0 0 0 0 0  οŽ–  .

Q8:

Evaluate 3 1 2 5 3 5 .

Q9:

3 2 = 3 2 = 3 2 Γ— 3 2 Γ— 3 2 = ο€» √ 3 2  = 2 = 8 3 5 1 5 1 5 1 5 1 5 1 5 1 5 5 + + 3 3 .

In general, π‘Ž π‘₯ 𝑦 means the π‘₯ th exponent of the 𝑦 th root of π‘Ž . So, 3 2 3 5 means β€œthe fifth root of 32, cubed”.

Evaluate 1 6 3 4 .

Q10:

Evaluate 2 5 6 1 4 .

Q11:

8 1 = 8 1 = ο€» √ 8 1  = 2 7 0 . 7 5 3 3 3 4 4 = ( 3 ) .

In this example we could see that 0.75 is equivalent to 3 4 so we need to calculate the cube of the fourth root of 81.

Evaluate 1 6 0 . 7 5 .

Q12:

2 1 6 = 2 1 6 = 2 1 6 = 2 1 6 Γ— 2 1 6 Γ— 2 1 6 = √ 2 1 6 Γ— √ 2 1 6 Γ— √ 2 1 6 1 + + 1 3 1 3 1 3 1 3 1 3 1 3 3 3 3 .

This is an example of using rational exponents to represent radicals. So, 2 1 6 1 3 means β€œthe cube root of 216” or 3 √ 2 1 6 .

Evaluate 2 7 1 3 .

Q13:

Evaluate 2 4 3 0 . 6 .

Q14:

Evaluate 6 4 1 3 .

Q15:

Evaluate 2 5 6 1 8 .

Q16:

Completely simplify 5 . 0 6 2 5 0 . 7 5 .

Q17:

Evaluate 1 0 0 0 0 0   .

Q18:

Evaluate 6 4 1 2 .

Q19:

Evaluate 3 2 2 5 .

Q20:

Evaluate ( 0 . 0 6 2 5 ) 0 . 2 5 .

Q21:

4 9 = 4 9 = 4 9 = ο€½ 4 9  = ο€» √ 4 9  1 ( ) Γ— 2 2 2 1 2 1 2 . This is an example of using rational exponents to represent radicals. So, 4 9 1 2 means β€œthe square root of 49” or √ 4 9 .

Evaluate 2 5 1 2 .

Q22:

ο€» π‘Ž 𝑏  𝑐 𝑑 means the 𝑐 th exponent of the 𝑑 th root of ο€» π‘Ž 𝑏  . In the example shown, we can evaluate the numerator and denominator separately.

ο€Ό 8 2 7  = 8 2 7 = ο€» √ 8  ο€» √ 2 7  = 2 3 = 4 9 2 3 2 3 2 3 3 3 2 2 2 2 .

Evaluate ο€Ό 3 2 2 4 3  3 5 .

Q23:

4 9 = 4 9 = 4 9 Γ— 4 9 = √ 4 9 Γ— √ 4 9 1 + 1 2 1 2 1 2 1 2 . This is an example of using rational exponents to represent radicals. So, 4 9 1 2 means β€œthe square root of 49” or √ 4 9 .

Evaluate 1 6 1 2 .

Q24:

Which of the following is equal to 9?

Q25:

Which of the following expressions is equivalent to 1 3 Γ— 1 3 Γ— 1 3 1 9 2 9 3 9 ?

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