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

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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).

User RSG
by
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