Answer:
1
Rewrite 200200 as its prime factors.
\sqrt[3]{2\times 2\times 2\times 5\times 5}32×2×2×5×5
2
Group the same prime factors into groups of three.
\sqrt[3]{(2\times 2\times 2)\times 5\times 5}3(2×2×2)×5×5
3
Rewrite each group of three in exponent form.
\sqrt[3]{{2}^{3}\times 5\times 5}323×5×5
4
Use this rule: \sqrt[3]{{x}^{3}}=x3x3=x.
2\sqrt[3]{5\times 5}235×5
5
Simplify.
2\sqrt[3]{25}2325
6
Rewrite 2525 as {5}^{2}52.
2\sqrt[3]{{5}^{2}}2352
7
Use this rule: {({x}^{a})}^{b}={x}^{ab}(xa)b=xab.
2\times {5}^{\frac{2}{3}}2×532
