Answer:
The value of [tex]64\sqrt[3]{x^{9} }[/tex] ÷ [tex]\sqrt[3]{64x^{6} }[/tex] is 16x.
Step-by-step explanation:
The nth root of 'x' can be written as
[tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex] where n is a integer.
[tex]\sqrt{xy} = \sqrt{x} *\sqrt{y}[/tex]
[tex]\sqrt[n]{x^{a} } = x^{\frac{a}{n} }[/tex]
Four cube is sixty four.
that is 4³ = 4×4×4 = 64
then [tex]\sqrt[3]{64} =(64)^{\frac{1}{3} } =(4^{3})^{\frac{1}{3} } = 4[/tex]
We have to find the value of [tex]64\sqrt[3]{x^{9} }[/tex] ÷ [tex]\sqrt[3]{64x^{6} }[/tex]
Given that [tex]64\sqrt[3]{x^{9} }[/tex] ÷ [tex]\sqrt[3]{64x^{6} }[/tex]
In general [tex]\sqrt[3]{x} = x^{\frac{1}{3} }[/tex]
[tex]\sqrt[3]{x^{9} } = x^{\frac{9}{3} } = x^{3}[/tex]
[tex]\sqrt[3]{64x^{6} } =(4^{3} )^{\frac{1}{3} }*(x^{6})^{\frac{1}{3} } } = 4x^{2}[/tex]
Now the expression becomes,
64x³÷ (4x²) = 16x
The value of [tex]64\sqrt[3]{x^{9} }[/tex] ÷ [tex]\sqrt[3]{64x^{6} }[/tex] is 16x.