![\frac{\sqrt[3]{20}}{5}](/tpl/images/1038/6751/d831e.png)
![x = \sqrt[3]{\frac{4}{25}}](/tpl/images/1038/6751/7042d.png)
, we proceed to show the procedure to determine the simplest form of this number:![\sqrt[3]{\frac{4}{25} }](/tpl/images/1038/6751/04b50.png)
Given.
Definition of cubic root.![[4\cdot (25)^{-1}]^{1/3}](/tpl/images/1038/6751/ef607.png)
Definition of division.![(4)^{1/3}\cdot [(25)^{-1}]^{1/3}](/tpl/images/1038/6751/e712b.png)
![\{(4)^{1/3}\cdot [(25)^{-1}]^{1/3}\} \cdot \{[(25)^{-1}]^{2/3}\cdot [(25)^{-1}]^{-2/3}\}](/tpl/images/1038/6751/2eaa7.png)
Modulative and associative properties/Existence of multiplicative inverse/
![\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot \{[(25)^{-1}]^{1/3}\cdot [(25)^{-1}]^{2/3}\}](/tpl/images/1038/6751/de8f3.png)
Commutative and associative properties![\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot (25)^{-1}](/tpl/images/1038/6751/787c0.png)
![[(4)^{1/3}\cdot (25)^{2/3}]\cdot (25)^{-1}](/tpl/images/1038/6751/b1156.png)
![[4\cdot (25)^{2}]^{1/3}\cdot (25)^{-1}](/tpl/images/1038/6751/0f1f2.png)
Definition of power and multiplication.![[(125)\cdot (20)]^{1/3}\cdot (25)^{-1}](/tpl/images/1038/6751/db241.png)
Definition of multiplication.![(125)^{1/3}\cdot [(20)^{1/3}\cdot (25)^{-1}]](/tpl/images/1038/6751/e0b20.png)
![5\cdot [(20)^{1/3}\cdot (25)^{-1}]](/tpl/images/1038/6751/83abb.png)
Definition of cubic root.![5\cdot [(20)^{1/3}\cdot (5)^{-1}\cdot (5)^{-1}]](/tpl/images/1038/6751/418a5.png)
Definition of multiplication/![[(20)^{1/3}\cdot (5)^{-1}][5\cdot (5)^{-1}]](/tpl/images/1038/6751/8b3b4.png)
Commutative and associative properties.
Existence of multiplicative inverse/Modulative propertySimply the expression in the simplest form
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Answers: 1
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