Answer:
[tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex]
Step-by-step explanation:
Let be [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex], this expression is simplified as follows:
1) [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex] Given
2) [tex]\sqrt[3]{4^{3}}-\sqrt[3]{2^{5}}\times \sqrt[3]{5^{3}}[/tex] Definition of power
3) [tex](4^{3})^{1/3}-(2^{2}\cdot 2^{3})^{1/3}\times (5^{3})^{1/3}[/tex] Definition of n-th root/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]
4) [tex]4 - (2^{2})^{1/3}\times 2\times 5[/tex] [tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4 - 10\times 4^{1/3}[/tex] Multiplication/Definition of power
6) [tex]4^{1/3}\cdot (4^{2/3}-10)[/tex] Distributive property/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]
7) [tex]\sqrt[3]{4}\times [(4^{2})^{1/3}-10][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Definition of n-th root
8) [tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex] Definition of power/Result
