Question
. Rewrite the expression as a product of identical factors to find the product for 100 3/2
. Submit your answer in simplified form and do not include a comma in your answer.(1 point)
100 3/2=
. Submit your answer in simplified form and do not include a comma in your answer.(1 point)
100 3/2=
Answers
GPT-4o mini
To rewrite \( 100^{3/2} \) as a product of identical factors, we can first express \( 100 \) in a more manageable form.
We know that:
\[
100 = 10^2
\]
So,
\[
100^{3/2} = (10^2)^{3/2}
\]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify this:
\[
(10^2)^{3/2} = 10^{2 \cdot \frac{3}{2}} = 10^{3}
\]
Now, \( 10^{3} = 10 \times 10 \times 10\).
Thus, \( 100^{3/2} = 10 \times 10 \times 10 \).
In simplified form:
\[
\boxed{10 \times 10 \times 10}
\] or, if you need a single result, \( 1000 \).
We know that:
\[
100 = 10^2
\]
So,
\[
100^{3/2} = (10^2)^{3/2}
\]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify this:
\[
(10^2)^{3/2} = 10^{2 \cdot \frac{3}{2}} = 10^{3}
\]
Now, \( 10^{3} = 10 \times 10 \times 10\).
Thus, \( 100^{3/2} = 10 \times 10 \times 10 \).
In simplified form:
\[
\boxed{10 \times 10 \times 10}
\] or, if you need a single result, \( 1000 \).