64 ³√x9 ÷ ³√64x6 please answer​

Answers 2

Step-by-step explanation:

64×9=576. 64×6=384. 576÷384=0.66666666666

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.

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