To solve the expression [tex]\(100^{\frac{3}{2}}\)[/tex], let's rewrite and simplify it in several steps.
1. Start with the given expression:
[tex]\[100^{\frac{3}{2}}\][/tex]
2. Recognize that the base [tex]\(100\)[/tex] can be expressed as [tex]\(10^2\)[/tex]:
[tex]\[(10^2)^{\frac{3}{2}}\][/tex]
3. Apply the power of a power property [tex]\((a^m)^n = a^{mn}\)[/tex]:
[tex]\[10^{2 \cdot \frac{3}{2}}\][/tex]
4. Simplify the exponent [tex]\(2 \cdot \frac{3}{2}\)[/tex]:
[tex]\[10^{3}\][/tex]
5. Calculate the final result:
[tex]\[10^3 = 1000\][/tex]
Therefore, the simplified form of [tex]\(100^{\frac{3}{2}}\)[/tex] is:
[tex]\[\boxed{1000}\][/tex]
