Understanding Radicals - Math
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Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
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To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by 
to remove the radical:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents:
Convert the radical to exponential notation.
Convert the radical to exponential notation.
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Remember that any term outside the radical will be in the denominator of the exponent.
Since 
does not have any roots, we are simply raising it to the one-fourth power.
Remember that any term outside the radical will be in the denominator of the exponent.
Since
What is the value of 
?
What is the value of
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An exponent written as a fraction can be rewritten using roots. 
can be reqritten as 
. The bottom number on the fraction becomes the root, and the top becomes the exponent you raise the number to. 
is the same as 
. This will give us the answer of 243.
An exponent written as a fraction can be rewritten using roots.
Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
Tap to see back →
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by 
to clear the square root:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents:
Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
Tap to see back →
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by 
to cancel the radical:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents:
Which fraction is equivalent to 
?
Which fraction is equivalent to
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Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Simplify the following radical. Express in rational (exponential) form.
Simplify the following radical. Express in rational (exponential) form.
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Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Choose the fraction equivalent to 
.
Choose the fraction equivalent to
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Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Multiply the numerator and denominator by the compliment of the denominator:
Simplify the expression:
Simplify the following radical. Express in rational (exponential) form.
Simplify the following radical. Express in rational (exponential) form.
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Multiply the numerator and denominator to the exponent:
Simplify the expression by combining like terms:
Multiply the numerator and denominator to the exponent:
Simplify the expression by combining like terms:
Simplify: 
Simplify:
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Multiply the numerator and denominator to the exponent:
Simplify the expression by combining like terms:
Multiply the numerator and denominator to the exponent:
Simplify the expression by combining like terms:
Express the following exponent in radical form:
Express the following exponent in radical form:
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Begin by converting each exponent to have a denominator of 
:
Now, rearrange into radical form:
Finally, simplify:
Begin by converting each exponent to have a denominator of
Now, rearrange into radical form:
Finally, simplify:
Express the following exponent in radical form:
Express the following exponent in radical form:
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Begin by converting each exponent to have a denominator of :
Now, put this in radical form:
Finally, simplify:
Begin by converting each exponent to have a denominator of
Now, put this in radical form:
Finally, simplify:
Express the following exponent in radical form:
Express the following exponent in radical form:
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Begin by changing the fractional exponents so that they both have a common denominator of 
:
Now, put this in radical form and simplify:
Begin by changing the fractional exponents so that they both have a common denominator of
Now, put this in radical form and simplify:
Simplify the following radical expression using exponents. Express the final answer in radical form.
Simplify the following radical expression using exponents. Express the final answer in radical form.
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Begin by converting the radical into exponent form:
Simplify the exponent and multiply:
Convert into radical form:
Simplify:
Begin by converting the radical into exponent form:
Simplify the exponent and multiply:
Convert into radical form:
Simplify:
Simplify the expression. Find the positive solution only.
Simplify the expression. Find the positive solution only.
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When working in square roots, each component can be treated separately.
Now, we can simplify each term.
Combine the simplified terms to find the answer. Anything outside of the square root is combined, while anything under the root is combined under the root.
When working in square roots, each component can be treated separately.
Now, we can simplify each term.
Combine the simplified terms to find the answer. Anything outside of the square root is combined, while anything under the root is combined under the root.
Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
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To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by to remove the radical:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents:
Convert the radical to exponential notation.
Convert the radical to exponential notation.
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Remember that any term outside the radical will be in the denominator of the exponent.
Since does not have any roots, we are simply raising it to the one-fourth power.
Remember that any term outside the radical will be in the denominator of the exponent.
Since
What is the value of ?
What is the value of
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An exponent written as a fraction can be rewritten using roots. can be reqritten as . The bottom number on the fraction becomes the root, and the top becomes the exponent you raise the number to. is the same as . This will give us the answer of 243.
An exponent written as a fraction can be rewritten using roots.
Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
Tap to see back →
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by to clear the square root:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents:
Express the following radical in rational (exponential) form:
Express the following radical in rational (exponential) form:
Tap to see back →
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by to cancel the radical:
Finally, simplify the exponents:
To convert the radical to exponent form, begin by converting the integer:
Now, divide each exponent by
Finally, simplify the exponents: