Question Video: Solving a Word Problem by Taking Powers of Rational Numbers | Nagwa Question Video: Solving a Word Problem by Taking Powers of Rational Numbers | Nagwa

# Question Video: Solving a Word Problem by Taking Powers of Rational Numbers Mathematics • First Year of Preparatory School

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Find an expression for the volume of the given cube whose side lengths are 2π₯/5.

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### Video Transcript

Find an expression for the volume of the given cube whose side lengths are two π₯ over five.

We begin by recalling that the volume of a cube is given by the cube of its side length. This means that if a cube has side length π, then its volume is π multiplied by π multiplied by π, which is π cubed. In this question, we are told that the side length is two π₯ over five. This means that its volume is given by the expression two π₯ over five cubed. Recalling that for any rational number π over π and any integer π π over π to the πth power is equal to π to the πth power divided by π to the πth power, our expression simplifies to two π₯ cubed over five cubed.

Next, we recall that to multiply monomials, we multiply the coefficients and add the powers of the shared variables. This means that two π₯ multiplied by two π₯ multiplied by two π₯ is equal to eight π₯ cubed. And since five cubed is 125, our expression simplifies to eight π₯ cubed over 125. This is an expression for the volume of a cube whose side lengths are two π₯ over five.

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