IXL | Powers of ten with negative exponents

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Learn with an example

question

Which of the following are equivalent to

1

1,000

?

Select all that apply.

10

–

3

1

10

–

10

3

10

3

key idea

A power of ten with a negative exponent can be written as a fraction. The numerator is 1, and the denominator is a power of ten with a positive exponent. For example,

10

–

2

=

1

10

2

You can also write powers of ten with negative exponents in several other equivalent ways. For example, you can write

10

–

2

in all of these ways:

10

–

2

=

1

10

2

=

1

10

=

1

10

1

10

=

1

100

=

0.01

solution

You were given

1

1,000

,

which is equivalent to

1

10

3

.

The numerator of this fraction is 1, and the denominator is a power of ten with a positive exponent.

So, you can write

1

1,000

as a power of ten with a negative exponent:

1

1,000

=

1

10

3

=

10

–

3

Here are several equivalent ways to write

10

–

3

:

10

–

3

=

1

10

3

=

1

10

=

1

10

1

10

1

10

=

1

1,000

=

0.001

So, these answer choices are equivalent to

1

1,000

:

10
–
3
1
10
10
10

The other answer choices are not equivalent to

1

1,000

.

–
10
3
is a negative number, but
1
1,000
is positive.
10
3
3
3
is not a power of ten, but
1
1,000
is.

Looking for more? Try these:

Lesson: Properties of exponents

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