Question

Show that each expression is equivalent to 2x. Assume x is a positive real number

6x^3/(3√27x^6)

Answer 1

Answer and explanation

We have given equation
`\frac{6x^3}{\sqrt[3]{27x^6}}`

We have to prove that after operation it will be equal to 2x

We know that cube root of 27 is 3

And cube root of
`x^6` is
`x^2`

So we can write the expression
`\frac{6x^3}{\sqrt[3]{27x^6}}=(6x^3)/(3x^2)=2x`

So after doing operation on the given expression the result will be 2x

Hence proved