The equivalent expression of the expression [tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex] is [tex](\frac{3x^2}{4y})^\frac 13[/tex]
The expression is given as:
[tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex]
Divide 12 in the expression by 4
[tex]\sqrt[3]{\frac{3x^2}{16y}}[/tex]
Divide 16 in the expression by 4
[tex]\sqrt[3]{\frac{3x^2}{4y}}[/tex]
Apply the power rule of indices
[tex](\frac{3x^2}{4y})^\frac 13[/tex]
Hence, the equivalent expression of [tex]\sqrt[3]{\frac{12x^2}{16y}}[/tex] is [tex](\frac{3x^2}{4y})^\frac 13[/tex]
Read more about equivalent expression at:
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