# Lesson Worksheet: Fractional Exponents Mathematics

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

Q1:

Simplify .

Q2:

Express in the form .

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Q3:

Evaluate .

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Q4:

Evaluate .

Q5:

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

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

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Q6:

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Q7:

Evaluate .

Q8:

Evaluate .

Q9:

.

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

Evaluate .

Q10:

Evaluate .

Q11:

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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:

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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 7.

Evaluate .

Q22:

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

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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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Q25:

Which of the following expressions is equivalent to ?

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