Answer:
[tex]a = 8[/tex] and [tex]b = 2[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{x^{10}}[/tex]
[tex]x = -2[/tex]
Required
Express as: [tex]a\sqrt[3]{b}[/tex]
Substitute -2 for x in [tex]\sqrt[3]{x^{10}}[/tex]
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{(-2)^{10}}[/tex]
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{1024}[/tex]
Express 1024 as 2^10
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{2^{10}}[/tex]
Apply law of indices:
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{2^{9+1}}[/tex]
Apply law of indices: Split
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{2^{9}*2^1}}[/tex]
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{2^{9}} *\sqrt[3]{2^1}}[/tex]
[tex]\sqrt[3]{x^{10}} = \sqrt[3]{2^{9}} *\sqrt[3]{2}}[/tex]
[tex]\sqrt[3]{x^{10}} = 2^{9*\frac{1}{3}}} *\sqrt[3]{2}}[/tex]
[tex]\sqrt[3]{x^{10}} = 2^3 *\sqrt[3]{2}}[/tex]
[tex]\sqrt[3]{x^{10}} = 8\sqrt[3]{2}}[/tex]
By comparison:
[tex]a = 8[/tex] and [tex]b = 2[/tex]
