IXL - Operations with rational exponents (Precalculus practice)

Simplify.

ref_doc_title.

Learn with an example

question

Simplify.

key idea

is a positive real number and

is an integer with

The same identity is also true if

is negative and

is odd. However, if

is negative and

is even then

and

do not exist.

is also an integer, this formula implies:

(

)

The symbol

is called a

radical.

the radical is a square root and the 2 is not written:

For non-zero real numbers

and

and a rational number

(

)

solution

The exponents are the same, so apply the property

(

)

to simplify the product.

(

)

Now, write the exponent using a radical and simplify further. It is good practice to write the expression as a radical raised to an exponent, using the identity

This way the numbers do not get too large.

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Not feeling ready yet? These can help:

T.3Multiplication with rational exponents

T.4Division with rational exponents

T.5Power rule

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