Rewrite the expression as a product of identical factors to find the product for 100^3/2, Simplify using the denominator of the exponent before applying the numerator on the exponent.

Question

. Submit your answer in simplified form.

Answer 1

To simplify the expression \( 100^{3/2} \), we can follow these steps:

1. Rewrite \( 100 \) as a base with an exponent: \[ 100 = 10^2 \] Thus, \[ 100^{3/2} = (10^2)^{3/2} \]

2. Now we apply the property of exponents \( (a^m)^n = a^{m \cdot n} \): \[ (10^2)^{3/2} = 10^{2 \cdot (3/2)} \] \[ = 10^{3} \]

3. Now, simplify \( 10^3 \): \[ 10^3 = 10 \times 10 \times 10 \]

Thus, the simplified expression for \( 100^{3/2} \) as a product of identical factors is: \[ 10 \times 10 \times 10 \]

So, the answer is: \[ 100^{3/2} = 10^3 = 1000 \]