# Worksheet: Fractional Exponents

In this worksheet, we will practice simplifying fractional indices.

**Q1: **

Simplify .

**Q2: **

Express in the form .

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**Q3: **

Evaluate .

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**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 in radical form.

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**Q6: **

Write in radical form.

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**Q7: **

Evaluate .

**Q8: **

Evaluate .

**Q9: **

.

In general, means the th exponent of the th root of . So, means “the fifth root of 32, cubed”.

Evaluate .

**Q11: **

.

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

Evaluate .

**Q12: **

.

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

Evaluate .

**Q13: **

Evaluate .

**Q14: **

Evaluate .

**Q15: **

Evaluate .

**Q16: **

Completely simplify .

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**Q17: **

Evaluate .

**Q18: **

Evaluate .

**Q19: **

Evaluate .

**Q20: **

Evaluate .

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**Q21: **

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

Evaluate .

**Q22: **

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

.

Evaluate .

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**Q23: **

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

Evaluate .

**Q24: **

Which of the following is equal to 9?

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