Rewrite the expression as a product of identical

Question

factors to find the product for
100
3/2 show ur work

Answer 1

To rewrite the expression \(100^{3/2}\) as a product of identical factors, we can follow these steps:

1. Rewrite the exponent:
   The exponent \(3/2\) can be expressed as follows: \[ 100^{3/2} = \left(100^{1/2}\right)^3 \]

2. Calculate \(100^{1/2}\):
   The square root of \(100\) is: \[ 100^{1/2} = \sqrt{100} = 10 \]

3. Substitute back into the equation:
   Now we can substitute \(10\) back into the exponent expression: \[ 100^{3/2} = (10)^3 \]

4. Calculate \(10^3\):
   Now we calculate \(10^3\): \[ 10^3 = 10 \times 10 \times 10 = 1000 \]

Thus, the product of \(100^{3/2}\) is: \[ \boxed{1000} \]

Summary of Steps:

1. \(100^{3/2} = (100^{1/2})^3\)
2. \(\sqrt{100} = 10\)
3. \((10)^3 = 1000\)
4. Final result: \(100^{3/2} = 1000\)