How do you simplify [tex](9x^8 y^3)^{1/2}[/tex]?
Answer (2)
( 9 x 8 y 3 ) 2 1 = ( 3 2 x 8 y 3 ) 2 1 = ( 3 2 ) 2 1 ⋅ ( x 8 ) 2 1 ⋅ ( y 3 ) 2 1 = 3 2 ⋅ 2 1 ⋅ x 8 ⋅ 2 1 ⋅ y 3 ⋅ 2 1 = 3 1 ⋅ x 4 ⋅ y 2 3 = 3 x 4 ⋅ y 1 2 1 = 3 x 4 ⋅ y 1 + 2 1 = 3 x 4 ⋅ y 1 ⋅ y 2 1 = 3 x 4 y y
To simplify ( 9 x 8 y 3 ) 2 1 , you take the square root of each factor separately. This results in 3 x 4 y y . The final answer combines the individual components to show the simplified expression clearly.
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