Question
Rational exponents practice rewrite the expression as a product of identical factors to find the product of 100 3 / 2 submit your answer
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Answered by
GPT-4o mini
To rewrite the expression \( 100^{3/2} \) as a product of identical factors, you can break it down as follows:
1. First, recognize that the exponent \( \frac{3}{2} \) can be expressed as \( (100^{1/2})^3 \).
2. The term \( 100^{1/2} \) is the square root of 100, which is 10. Therefore, we can express this as:
\[
100^{3/2} = (100^{1/2})^3 = (10)^3
\]
3. Now, calculate \( 10^3 \):
\[
10^3 = 10 \times 10 \times 10 = 1000
\]
Thus, the product \( 100^{3/2} = 1000 \).
So, the answer is:
\[
\boxed{1000}
\]
1. First, recognize that the exponent \( \frac{3}{2} \) can be expressed as \( (100^{1/2})^3 \).
2. The term \( 100^{1/2} \) is the square root of 100, which is 10. Therefore, we can express this as:
\[
100^{3/2} = (100^{1/2})^3 = (10)^3
\]
3. Now, calculate \( 10^3 \):
\[
10^3 = 10 \times 10 \times 10 = 1000
\]
Thus, the product \( 100^{3/2} = 1000 \).
So, the answer is:
\[
\boxed{1000}
\]