Respuesta :
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: [tex] \\8x^{9}[/tex]
Step-by-step explanation:
One way
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]
[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]
[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]
[tex] \\8x^{9}[/tex]
This is the first simplification.
Second way
Simplify the terms inside parentheses, and then raise the result to the third power.
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]
[tex] \\ (2*x^{5-2})^{3}[/tex]
[tex] \\ (2*x^{3})^{3}[/tex]
[tex] \\ (2^{3}*x^{3*3})[/tex]
[tex] \\ (8*x^{9})[/tex]
or [tex] \\ 8x^{9}[/tex].
