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: $\\8x^{9}$

Step-by-step explanation:

One way

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

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{64x^{5*3}}{8x^{2*3}})$

$\\ (\frac{64x^{15}}{8x^{6}})$

$\\ \frac{64}{8}\frac{x^{15}}{x^{6}}$

$\\8x^{9}$

This is the first simplification.

Second way

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

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}$

$\\ (2*x^{5-2})^{3}$

$\\ (2*x^{3})^{3}$

$\\ (2^{3}*x^{3*3})$

$\\ (8*x^{9})$

or $\\ 8x^{9}$.