Answer :

Sure! Let's break down the given expression step-by-step to understand how it can be solved:

The original expression to simplify is:
[tex]\[ \frac{5 \sqrt[3]{54}}{3 \sqrt[3]{40}} \][/tex]

### Step 1: Calculate the cube roots

First, we need to calculate the cube root of 54 and the cube root of 40.

- Cube root of 54: [tex]\( \sqrt[3]{54} \approx 3.7797631496846193 \)[/tex]
- Cube root of 40: [tex]\( \sqrt[3]{40} \approx 3.4199518933533937 \)[/tex]

### Step 2: Multiply by respective constants

Next, we multiply the cube root of 54 by 5 and the cube root of 40 by 3 to get the numerator and the denominator respectively.

- Numerator: [tex]\( 5 \times 3.7797631496846193 \approx 18.898815748423097 \)[/tex]
- Denominator: [tex]\( 3 \times 3.4199518933533937 \approx 10.25985568006018 \)[/tex]

### Step 3: Form the fraction

Now, we form the fraction with the calculated numerator and denominator:

[tex]\[ \frac{18.898815748423097}{10.25985568006018} \][/tex]

### Step 4: Simplify the fraction

Finally, we perform the division to simplify the fraction:

[tex]\[ \frac{18.898815748423097}{10.25985568006018} \approx 1.8420157493201934 \][/tex]

### Conclusion

Therefore, the simplified result of the given expression [tex]\( \frac{5 \sqrt[3]{54}}{3 \sqrt[3]{40}} \)[/tex] is approximately:

[tex]\[ 1.8420157493201934 \][/tex]