Question

How can (4x⁵/2x²)³ be solved in 2 different ways

Answer 1

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same:
`\\8x^(9)`

Explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

`\\ ((4x^(5))/(2x^(2)))^(3)`

`\\ ((64x^(5*3))/(8x^(2*3)))`

`\\ ((64x^(15))/(8x^(6)))`

`\\ (64)/(8)(x^(15))/(x^(6))`

`\\8x^(9)`

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

`\\ ((4x^(5))/(2x^(2)))^(3)`

`\\ ((4)/(2)*(x^(5))/(x^(2)))^(3)`

`\\ (2*x^(5-2))^(3)`

`\\ (2*x^(3))^(3)`

`\\ (2^(3)*x^(3*3))`

`\\ (8*x^(9))`

or
`\\ 8x^(9)`.