Questions: (5x/y)^3

Transcript text: $\left(\frac{5 x}{y}\right)^{3}$

Solution

Solution Steps

To solve the expression $\left(\frac{5x}{y}\right)^{3}$, we need to compute the cube of the fraction $\frac{5x}{y}$. This involves raising both the numerator and the denominator to the power of 3.

Step 1: Understand the Expression

The expression given is $\left(\frac{5x}{y}\right)^{3}$. We need to evaluate this expression for specific values of $x$ and $y$.

Step 2: Substitute Values

Substitute $x = 2$ and $y = 3$ into the expression: \[ \left(\frac{5 \times 2}{3}\right)^{3} = \left(\frac{10}{3}\right)^{3} \]

Step 3: Calculate the Cube

Calculate the cube of $\frac{10}{3}$: \[ \left(\frac{10}{3}\right)^{3} = \frac{10^3}{3^3} = \frac{1000}{27} \]

Step 4: Simplify the Result

Convert $\frac{1000}{27}$ to a decimal: \[ \frac{1000}{27} \approx 37.0370 \]

Final Answer

The value of the expression $\left(\frac{5x}{y}\right)^{3}$ when $x = 2$ and $y = 3$ is $\boxed{37.0370}$.

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