To rewrite the expression \( 100^{\frac{3}{2}} \) as a product of identical factors, we can first break it down:
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Rewrite \( 100 \) as \( 10^2 \): \[ 100^{\frac{3}{2}} = (10^2)^{\frac{3}{2}} \]
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Apply the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \): \[ (10^2)^{\frac{3}{2}} = 10^{2 \cdot \frac{3}{2}} = 10^3 \]
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Now, calculate \( 10^3 \): \[ 10^3 = 10 \times 10 \times 10 \]
Thus, \( 100^{\frac{3}{2}} \) can be rewritten as \( 10 \times 10 \times 10 \).
Finally, the product \( 100^{\frac{3}{2}} = 1000 \).
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