Which expression is a perfect cube?

-1,331m¹⁸n¹⁵p²¹ = (-11m⁶n⁵p⁷)³

Step-by-step explanation:

The cube root of 1452 is about 11.32371348 It is not a perfect cube. The cube root of 1331 is 11, so the cube root of -1331 is -11. Either way, the number ±1331 is a perfect cube.

In order for the constellation of variables to be a perfect cube, all the exponents need to be multiples of 3. 22 is not a multiple of 3.

These criteria eliminate the 1st, 3rd, and 4th answer choices, leaving only the 2nd choice.

JK = 234

Concept:

Here, we need to know the idea of the segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

JL = 8x - 3

LK = 4x + 57

Given expression deducted from the given figure

JL = LK

Substitute values into the expression

8x - 3 = 4x + 57

Add 3 on both sides

8x - 3 + 3 = 4x + 57 + 3

8x = 4x + 60

Subtract 4x on both sides

8x - 4x = 4x + 60 - 4x

4x = 60

Divide 4 on both sides

4x / 4 = 60 / 4

x = 15

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Given information

JL = 8x - 3

LK = 4x + 57

x = 15

Given expression deducted from the segment addition postulate

JK = JL + LK

Substitute values into the expression

JK = 8x - 3 + 4x + 57

JK = 8(15) - 3 + 4(15) + 57

Simplify by multiplication

JK = 120 - 3 + 60 + 57

Simplify by simple operation (addition/subtraction)

JK = 117 + 60 + 57

JK = 177 + 57

Hope this helps!! :)

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