IXL - Identify equivalent exponential expressions I (Algebra 1 practice)

Which expression is equivalent to

(

)

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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

(

)

Use the identity

(

)

So,

(

)

is equal to

Step 2: Now write each answer choice in the form

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.

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 equal to

The expressions

and

(

)

are

equivalent.

The correct answer is

Looking for more? Try these:

Lesson: Properties of exponents

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Work it out

Not feeling ready yet? These can help:

C.6Understanding negative exponents

R.4Multiplication rule for exponents

R.5Division rule for exponents

R.6Power rule for exponents

Lesson: Properties of exponents

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