Respuesta :

Hagrid
To make the monomial 125 x^18 y^3 z^25 a perfect cube, the entire expression should be reduced to a rational number when the cube root is taken. For the constant 125, the cube root is 5, so it doesn't need to be changed. For the variables, the exponents should be divisible by 3. The exponent of z is not divisible by 3. It can be subtracted with 1 or added with 2 to make the expression a perfect cube.
Eduard22sly

The number in the monomial 125x¹⁸y³z²⁵ that needs to be changed to make the expression a perfect cube is 25

Data obtained from the question

  • Monomial = 125x¹⁸y³z²⁵
  • Number to be changed =?

How to determine the number to be changed

To determine the number to be changed in order to obtained a perfect cube, we shall determine the cube root of each entity. This is illustrated below

Cube root of 125

³√125 = 5

Cube root of x¹⁸

³√x¹⁸ = x⁶

Cube root of y³

³√y³ = y

Cube root of z²⁵

³√z²⁵ = z^(25/3)

From the illustration above, we can see that 25 is not a perfect cube.

Thus, 25 needs to be changed in order for the expression 125x¹⁸y³z²⁵ to be a perfect cube

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