IXL | Identify equivalent expressions involving exponents I

Which expression is equivalent to

(

)

ref_doc_title.

Learn with an example

question

Which expression is equivalent to

key idea

Properties of exponents

For nonzero integers

and

and integer exponents

and

a
1
=
a
a
0
=
1
1
a
x
=
a
–
x
a
x
a
y
=
a
x
+
y
a
x
a
y
=
a
x
–
y
(
a
x
)
y
=
a
x
y
a
x
b
x
=
(
a
b
)
x
a
x
b
x
=
i
a
b
i
x

solution

To find which expression is equivalent to

write each expression with the same base.

The answer choices and

can all be written as a power of 4. So, use properties of exponents to write each expression in the form

Then, see which one matches

in this form.

Step 1: Write

in the form

Use the identity

So,

is equal to

Step 2: Now write each answer choice in the form

Write

in the form

Use the identity

–

Use the identity

–

So,

is equal to

–

but

is not. (It is equal to

The expressions

and

are not

equivalent.

The expression

is in the form

You've already found that

is not equal to

(It is equal to

The expressions

and

are not

equivalent.

The expression

is in the form

You've already found that

is equal to

The expressions

and

are

equivalent.

Write

in the form

Use the identity

–

Use the identity

–

So,

is equal to

–

but

is not. (It is equal to

The expressions

and

are not

equivalent.

The correct answer is

Looking for more? Try these:

Lesson: Properties of exponents

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Teacher tools

Work it out

Not feeling ready yet? These can help:

C.6Understanding negative exponents

C.12Power of a power: integer bases

C.10Divide powers: integer bases

C.9Multiply powers: integer bases

Lesson: Properties of exponents

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