Question

Simplify the expression
`((64x^(12) )/(125x^(3) ) )^{(1)/(3) }` . Assume all variables are positive

Answer 1

To simplify the expression
`\left((64x^(12))/(125x^(3))\right)^{(1)/(3)}`, we can start by simplifying the numerator and denominator separately.

In the numerator, we have
`64x^(12)`. We can rewrite 64 as
`4^3` and
`x^(12)` as
`(x^3)^4`. So, the numerator becomes
`4^3 \cdot (x^3)^4`.

In the denominator, we have
`125x^(3)`. We can rewrite 125 as
`5^3` and
`x^(3)` as
`(x^3)^1`. So, the denominator becomes
`5^3 \cdot (x^3)^1`.

Now, let's simplify the expression inside the parentheses:
`4^3 \cdot (x^3)^4 / (5^3 \cdot (x^3)^1)`.

Simplifying each part further, we have:

`4^3 = 64`,

`(x^3)^4 = x^(12)`,

`5^3 = 125`, and

`(x^3)^1 = x^3`.

Now the expression becomes:

`(64x^(12))/(125x^3)`.

To simplify further, we can cancel out the common factors in the numerator and denominator. Both 64 and 125 have a common factor of 5, and x^12 and x^3 have a common factor of x^3. Canceling these common factors, we get:

`(64x^(12))/(125x^3) = (8)/(5) \cdot (x^(12))/(x^3) = (8)/(5)x^(12-3) = (8)/(5)x^9`.

Therefore, the simplified expression is
`(8)/(5)x^9`.

`\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}`

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