Radicals - Math

Begin by multiplying the numerator and denominator by the complement of the denominator:

Combine like terms and simplify:

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:

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.

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.

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 to cancel the radical:

Finally, simplify the exponents:

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:

Multiply the numerator and denominator by the compliment of the denominator:

Simplify the expression:

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:

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, put this in radical form:

Finally, simplify:

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 converting the radical into exponent form:

Simplify the exponent and multiply:

Convert into radical form:

Simplify:

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.

To solve this equation, we have to factor our radicals. We do this by finding numbers that multiply to give us the number within the radical.

Add them together:

4 is a perfect square, so we can find the root:

Since both have the same radical, we can combine them:

Use the multiplication property of radicals to split the fourth roots as follows:

Simplify the new roots:

Begin by factoring the integer:

Now, simplify the exponents:

Begin by converting the radical into exponent form:

Now, multiply the exponents: