Question

Write 2
3
·5
3
using a single exponent.
Now that you’ve rewritten this expression as repeated factors of 10, you can write this expression using an exponent. How can you show 3 factors of 10 using an exponent?
2
3

·
5
3

=
2
·
2
·
2
·
5
·
5
·
5
=
(2
·
5)
·
(2
·
5)
·
(2
·
5)
=
10

·
10
·
10
=
10

Answer 1

To express the expression \( 2^3 \cdot 5^3 \) using a single exponent, you can start by rewriting it in terms of the base 10:

1. First, write out the expression:
\[
2^3 \cdot 5^3 = (2 \cdot 2 \cdot 2) \cdot (5 \cdot 5 \cdot 5)
\]

2. Group the factors together:
\[
= (2 \cdot 5) \cdot (2 \cdot 5) \cdot (2 \cdot 5)
\]

3. Notice that \( 2 \cdot 5 = 10 \):
\[
= 10 \cdot 10 \cdot 10
\]

4. This can now be expressed as:
\[
= 10^3
\]

So the original expression \( 2^3 \cdot 5^3 \) can be rewritten as:
\[
2^3 \cdot 5^3 = 10^3
\]