Question

Gina estimates that her mom truck waits about 6000 pounds how can you write 6000 using exponents

Answer 1

To write 6000 using exponents, you can factor it into its prime components and then express those factors as exponents.

First, the prime factorization of 6000 is:
\[
6000 = 6 \times 1000
\]
\[
1000 = 10^3
\]
And since \(6 = 2 \times 3\), we can express this as:
\[
6000 = 6 \times 10^3 = (2 \times 3) \times (10^3)
\]

Now, since \(10 = 2 \times 5\), we substitute:
\[
10^3 = (2 \times 5)^3 = 2^3 \times 5^3
\]

Putting it all together:
\[
6000 = 2^1 \times 3^1 \times 2^3 \times 5^3
\]
Combining the \(2\) terms:
\[
6000 = 2^{1+3} \times 3^1 \times 5^3 = 2^4 \times 3^1 \times 5^3
\]

So, 6000 can be expressed as:
\[
6000 = 2^4 \times 3^1 \times 5^3
\]

This is one way to represent 6000 using exponents!