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Determine the results of the following operations​

Determine the results of the following operations​-example-1

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Answer:


\sqrt[3]{4}* (\sqrt[3]{16}-10 )

Explanation:

Let be
\sqrt[3]{64}-\sqrt[3]{32} * \sqrt[3]{125}, this expression is simplified as follows:

1)
\sqrt[3]{64}-\sqrt[3]{32} * \sqrt[3]{125} Given

2)
\sqrt[3]{4^(3)}-\sqrt[3]{2^(5)}* \sqrt[3]{5^(3)} Definition of power

3)
(4^(3))^(1/3)-(2^(2)\cdot 2^(3))^(1/3)* (5^(3))^(1/3) Definition of n-th root/
a^(b+c)= a^(b)\cdot a^(c)/
(a^(b))^(c) = a^(b\cdot c)

4)
4 - (2^(2))^(1/3)* 2* 5
a^(b+c)= a^(b)\cdot a^(c)/
(a\cdot b)^(c) = a^(c)\cdot b^(c)

5)
4 - 10* 4^(1/3) Multiplication/Definition of power

6)
4^(1/3)\cdot (4^(2/3)-10) Distributive property/
a^(b+c)= a^(b)\cdot a^(c)

7)
\sqrt[3]{4}* [(4^(2))^(1/3)-10]
(a^(b))^(c) = a^(b\cdot c)/Definition of n-th root

8)
\sqrt[3]{4}* (\sqrt[3]{16}-10 ) Definition of power/Result

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