IXL - Power rule (Algebra 2 practice)

Simplify. Assume all variables are positive.

(

)

Write your answer in the form A or

where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

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Learn with an example

question

Simplify. Assume all variables are positive.

(

)

Write your answer in the form A or

where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

key idea

For non-zero real numbers

and

and rational numbers

and

the following identities hold:

a
p
a
q
=
a
p
+
q
(
a
p
)
q
=
a
p
q
(
a
b
)
q
=
a
q
b
q
a
–
q
=
1
a
q
a
p
a
q
=
a
p
–
q
i
a
b
i
q
=
a
q
b
q

For a positive real number

and non-zero integers

and

with

The same identity is also true if

is negative and

is odd. However, if

is negative and

is even, then

does not exist and the identity does not hold.

solution

Use exponent rules to simplify the expression.

(

)

Use the identity

(

)

Use the identity

(

)

Looking for more? Try these:

Lesson: Rational exponents

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Teacher tools

Work it out

Not feeling ready yet? These can help:

T.1Evaluate rational exponents

R.10Simplify exponential expressions using the power rule

R.3Negative exponents

Lesson: Rational exponents

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