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grin007 [14]
2 years ago
13

Simply the expression in the simplest form​

Mathematics
1 answer:
nirvana33 [79]2 years ago
6 0

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

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