Worksheet: Fractional Exponents
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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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 7.
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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