IXL | Identify equivalent expressions involving exponents II

Select all the expressions that are equivalent to

–

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Learn with an example

question

Select all the expressions that are 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 expressions are equivalent to

–

write each expression with the same base.

The answer choices and

–

can all be written as a power of 3. So, use properties of exponents to write each expression in the form

Then, see which ones match

–

in this form.

Step 1: Write

–

in the form

–

Use the identity

(

)

–

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

–

Both

and

–

are equal to

–

The expressions

and

–

are

equivalent.

You've already found that

–

is not equal to 3. (It is equal to

–

The expressions 3 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.

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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C.14Identify equivalent expressions involving exponents I

Lesson: Properties of exponents

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