Question

Simply the expression in the simplest form​

Answer 1

Answer:

$\frac{\sqrt[3]{20}}{5}$

Step-by-step explanation:

Let $x = \sqrt[3]{\frac{4}{25}}$, we proceed to show the procedure to determine the simplest form of this number:

1) $\sqrt[3]{\frac{4}{25} }$ Given.

2) $\left(\frac{4}{25}\right)^{1/3}$ Definition of cubic root.

3) $[4\cdot (25)^{-1}]^{1/3}$ Definition of division.

4) $(4)^{1/3}\cdot [(25)^{-1}]^{1/3}$  $a^{c}\cdot b^{c} = (a\cdot b)^{c}$

5) $\{(4)^{1/3}\cdot [(25)^{-1}]^{1/3}\} \cdot \{[(25)^{-1}]^{2/3}\cdot [(25)^{-1}]^{-2/3}\}$ Modulative and associative properties/Existence of multiplicative inverse/$a^{b}\cdot a^{c} = a^{b+c}$

6) $\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot \{[(25)^{-1}]^{1/3}\cdot [(25)^{-1}]^{2/3}\}$ Commutative and associative properties

7) $\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot (25)^{-1}$  $a^{b}\cdot a^{c} = a^{b+c}$

8) $[(4)^{1/3}\cdot (25)^{2/3}]\cdot (25)^{-1}$  $(a^{b})^{c} = a^{b\cdot c}$

9) $[4\cdot (25)^{2}]^{1/3}\cdot (25)^{-1}$ $(a^{b})^{c} = a^{b\cdot c}$/$a^{c}\cdot b^{c} = (a\cdot b)^{c}$

10) $(2500)^{1/3}\cdot (25)^{-1}$ Definition of power and multiplication.

11) $[(125)\cdot (20)]^{1/3}\cdot (25)^{-1}$ Definition of multiplication.

12) $(125)^{1/3}\cdot [(20)^{1/3}\cdot (25)^{-1}]$ $a^{c}\cdot b^{c} = (a\cdot b)^{c}$/Associative property.

13) $5\cdot [(20)^{1/3}\cdot (25)^{-1}]$ Definition of cubic root.

14) $5\cdot [(20)^{1/3}\cdot (5)^{-1}\cdot (5)^{-1}]$ Definition of multiplication/$a^{c}\cdot b^{c} = (a\cdot b)^{c}$

15) $[(20)^{1/3}\cdot (5)^{-1}][5\cdot (5)^{-1}]$ Commutative and associative properties.

16) $(20)^{1/3}\cdot (5)^{-1}$ Existence of multiplicative inverse/Modulative property

17) $\frac{\sqrt[3]{20}}{5}$ Definitions of cubic root and division/Result