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\left(\sqrt[3]{1000}\right)^{2}
Use the rules of exponents to simplify the expression.
1000^{\frac{1}{3}\times 2}
To raise a power to another power, multiply the exponents.
1000^{\frac{2}{3}}
Multiply \frac{1}{3} times 2.
100
Raise 1000 to the power \frac{2}{3}.