Question

Evaluate the expression below when x = 6 and y = 2. 6 x 2/y 3

Answer 1

27

Explanation:

To evaluate an expression we need to find the numerical value of the expression by substituting appropriate values for the variables and performing the indicated mathematical operations.

Given rational expression:

`(6x^2)/(y^3)`

To evaluate the given expression when x = 6 and y = 2, substitute x = 6 and y = 2 into the expression and solve.

`(6(6)^2)/((2)^3)`

Following the order of operations, begin by evaluating the exponents first.

To square a number, we multiply it by itself.

`\implies 6^2 = 6 * 6 = 36`

To cube a number, we multiply it by itself twice.

`\implies 2^3 = 2 * 2 * 2 = 8`

Therefore:

`(6(6)^2)/((2)^3)=(6 \cdot 36)/(8)`

Multiply the numbers in the numerator:

`(216)/(8)`

Finally, divide 218 by 8:

`(216)/(8)=27`

Therefore, the evaluation of the given expression when x = 6 and y = 2 is 27.

`\hrulefill`

As one calculation:

`\begin{aligned}x=6, y=2 \implies (6x^2)/(y^3)&=(6(6)^2)/((2)^3)\\\\&=(6 \cdot 36)/(8)\\\\&=(216)/(8)\\\\&=27\end{aligned}`