64g4y4364g4y4\sqrt[3]{64{g}^{4}{y}^{4}}\sqrt{64{g}^{4}{y}^{4}}
1
Use this rule: ab=ab\sqrt{ab}=\sqrt{a}\sqrt{b}.
64g4y4364g4y4\sqrt[3]{64{g}^{4}{y}^{4}}\sqrt{64}\sqrt{{g}^{4}}\sqrt{{y}^{4}}

2
Since 8×8=648\times 8=64, the square root of 6464 is 88.
64g4y43×8g4y4\sqrt[3]{64{g}^{4}{y}^{4}}\times 8\sqrt{{g}^{4}}\sqrt{{y}^{4}}

3
Simplify  g4\sqrt{{g}^{4}}  to  g2{g}^{2}.
64g4y43×8g2y4\sqrt[3]{64{g}^{4}{y}^{4}}\times 8{g}^{2}\sqrt{{y}^{4}}

4
Simplify  y4\sqrt{{y}^{4}}  to  y2{y}^{2}.
64g4y43×8g2y2\sqrt[3]{64{g}^{4}{y}^{4}}\times 8{g}^{2}{y}^{2}

5
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
643g43y43×8g2y2\sqrt[3]{64}\sqrt[3]{{g}^{4}}\sqrt[3]{{y}^{4}}\times 8{g}^{2}{y}^{2}

6
Calculate.
4g43y43×8g2y24\sqrt[3]{{g}^{4}}\sqrt[3]{{y}^{4}}\times 8{g}^{2}{y}^{2}

7
Use this rule: (xa)b=xab{({x}^{a})}^{b}={x}^{ab}.
4g43y43×8g2y24{g}^{\frac{4}{3}}\sqrt[3]{{y}^{4}}\times 8{g}^{2}{y}^{2}

8
Use this rule: (xa)b=xab{({x}^{a})}^{b}={x}^{ab}.
4g43y43×8g2y24{g}^{\frac{4}{3}}{y}^{\frac{4}{3}}\times 8{g}^{2}{y}^{2}

9
Take out the constants.
(4×8)g43g2y43y2(4\times 8){g}^{\frac{4}{3}}{g}^{2}{y}^{\frac{4}{3}}{y}^{2}

10
Simplify  4×84\times 8  to  3232.
32g43g2y43y232{g}^{\frac{4}{3}}{g}^{2}{y}^{\frac{4}{3}}{y}^{2}

11
Use Product Rule: xaxb=xa+b{x}^{a}{x}^{b}={x}^{a+b}.
32g43+2y43+232{g}^{\frac{4}{3}+2}{y}^{\frac{4}{3}+2}

12
Simplify  43+2\frac{4}{3}+2  to  103\frac{10}{3}.
32g103y10332{g}^{\frac{10}{3}}{y}^{\frac{10}{3}}

Done
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