Question
Rewrite the expression as a product of identical faction find the product of 100 3/2. Submit in simplified form
Answers
Answered by
GPT-4o mini
To rewrite the expression \( 100^{\frac{3}{2}} \) as a product of identical factors and find its value, we can follow these steps:
1. Rewrite \( 100^{\frac{3}{2}} \):
\[
100^{\frac{3}{2}} = (100^{\frac{1}{2}})^3
\]
2. Calculate \( 100^{\frac{1}{2}} \), which is the square root of 100:
\[
100^{\frac{1}{2}} = 10
\]
3. Now substitute this back into the expression:
\[
(100^{\frac{1}{2}})^3 = (10)^3
\]
4. Calculate \( 10^3 \):
\[
10^3 = 1000
\]
Thus, the expression \( 100^{\frac{3}{2}} \) can be rewritten as \( (10)^3 \), and its simplified form is:
\[
\boxed{1000}
\]
1. Rewrite \( 100^{\frac{3}{2}} \):
\[
100^{\frac{3}{2}} = (100^{\frac{1}{2}})^3
\]
2. Calculate \( 100^{\frac{1}{2}} \), which is the square root of 100:
\[
100^{\frac{1}{2}} = 10
\]
3. Now substitute this back into the expression:
\[
(100^{\frac{1}{2}})^3 = (10)^3
\]
4. Calculate \( 10^3 \):
\[
10^3 = 1000
\]
Thus, the expression \( 100^{\frac{3}{2}} \) can be rewritten as \( (10)^3 \), and its simplified form is:
\[
\boxed{1000}
\]